In Tolkien's writings we find a few hints as to what differences there exist between the usage and pronunciation of the Sindarin of Gondor and the purer Elvish variety of that language. This article assumes the reader has a basic knowledge of the Sindarin language.
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1. Phonology and Pronunciation
     nþ, ŋχ, mφ, lþ - ch - y - mh
2. Grammar
3. Vocabulary
      attested - reconstructed

• • •

1. Phonology and Pronunciation

nþ, ŋχ, mφ, lþ
The Sindarin dialects that survived the 1st Age originally had the clusters nþ (nth), ŋχ (nch), mφ (mf, bilabial) and lþ (lth).
These were restopped to nt, ŋk, mp, lt in the end of words but everywhere else they normally turned to long nn, ŋŋ, mm, ll (voiceless at first, then for the greatest part voiced), but since the spelling was not normally changed the Gondorians reintroduced the spirants [cf. VT42:27 and various notes in PE17]. Thus we have to substitute nn, ng (ŋŋ), mm, ll with nth, nch, mf, lth on many occassions. For this cf. reconstructed vocabulary and grammar.
Note however that in the King's Letter [SD:129-31] we find ennas and suilannad, not **enthas, *suilanthad . Our supposed etymology of *enta-ssē may be wrong, but suilannad obviously has anna-, which corresponds to Quenya anta- and is in fact in PE17:93 given as anha-, older antha-. So either Tolkien had simply not yet come up with the idea or these forms may be due to the noble and courtly style of King Elessar, using 'pure' Eldarin pronunciation (as he certainly was used to from living in Imladrist) which would also explain his use of archaic mh for regular v.

Besides this fundamental phonological difference the differences in Gondorian pronunciation are quite obviously intended to avoid the Sindarin sounds not found in modern English. This way English readers of Tolkien's novels would in their pronunciation not differ from Elvish Sindarin more than the Gondorians would.

ch
Westron does not know the spirant ch [UT, Part Three, II, iv, n. 49] and thus Gondorians —with Westron being their native language— normally weakened the sound to h everywhere accept finally [LotR, App. E], which may be observed in the Gondorian terms Rohan, Rohirrim, where Tolkien informs us that these derive from S roch, horse, and that the 'proper' forms were Rochand/Rochan, Rochír-rim/Rochirrim [UT, Part Three, II, iv, n. 49].
This seems to suggest, that at the end of words we find -ch nevertheless, but then the note in UT informs us, that in this position the spirant is in fact turned to the stop k, so that we would find e.g. roc for horse. Furthermore this pronunciation does not seem to be represented in Tengwar writing (i.e. it is not in any of the King's Letter drafts, but there Elessar seems to have used Eldarin style anyway; cf. nþ,... above), but should of course in any case be kept in mind when creating a Neo-Sindarin text of Gondorian dialect.
Note that this avoiding of ch appears to conflict with Tolkien's ideas ng > nch (where from ŋk) if we are not to believe that the actual pronunciation of, say, enchui is in fact [ˈɛŋhʊi] rather than [ˈɛŋχʊi].

y
There appears to be no vowel y in the Common Speech, so that this also is in Gondorian Sindarin replaced by a sound Westron does know, namely i [LotR, App. E]. This means that in Gondorian pronunciation we could without context not tell between eryn (forest) and erin (on the), both being pronounced like the latter. Possibly this pronunciation is also not represented in Tengwar writing, which may be suggested by mhellyn in the King's Letter [SD], but to that source cf. nþ,... above.

mh
As pointed out, Tengwar transcription (at least of the King's Letter) need not tell very much, but the use of mh (instead of v) for lenited m in the word mhellyn (friends) [King's Letter, IX] might possibly point to an archaic pronunciation in this point (but cf. nþ,... above).

• • •

2. Grammar

In Noldorin the regular plural of orod was ereid or shortened ered. This conception seems to have stood for quite some time as it is still found in very many names on the maps in the Lord of the Rings (Ered Nimrais, Ered Lithui, Ered Mithrin,...). But later Tolkien seems to have changed his mind, since in sources from the 1960's (cf. WJ) forms like Eryd Luin are found, fitting perfectly well to the changed scenario in which e.g. the plural of goloð was no longer geleið but gelyð.
But the earlier forms were here to stay as they already appeared in the LotR, so what could Tolkien do? He might explain these forms as being dialectal maybe, and in Letters, no.168 (September 1955), Tolkien in fact explains that ened would likely be the Gondorian plural of onod, though regularly enyd would be found.
This is of course no direct prove of my assumption concerning ered, but it makes very clear that the regular plural change o > y did not normally occur in Gondorian Sindarin where much rather o > e was found. This might be due to the general incapability to pronounce y, but instead of simply pronouncing it as i (cf. phonology above) the (generally possible?) alternative forms became the only ones commonly being used in Gondor.
So we would for instance find:

Golodh (Ñoldo) > *Geledh (Ñoldor) | regularly Gelydh (cf. Annon-in-Gelydh)
Rodon (Vala) > *Roden (Valar) | regularly Rodyn (cf. Dor-Rodyn)
doron (oak) > deren (oaks) | regularly *deryn (the regular pl. of this N. form would thus also be regular in Gondorian S.)

This might possibly hint at a greater amount of simplification and analogy as would only seem probable, given that the speech of the mortals would certainly be much more changeful than that of the Elves. So when trying to write in Gondorian style Sindarin it appears advisable to use the most modern and analogical forms we can find. Among those would possibly be:

Analogical instead of archaic plural formations
Where syllabic liquids have developed a vowel this should possibly be treated as if it were archaic. Irregular plurals arising through loss of a consonant should likely also be regularized:
    • ogol (evil) > *egyl, *egel | regularly eigil [PE17:148,49]
    • naugol (dwarf) > *naugyl, *naugel (dwarves) | regularly nauglin, *naugil
    • thêl (sister) > *thîl (sisters) | regularly thelei (< *thelehi)
    • ...

Analogical instead of archaic mutations
Lenitions of b, d, g should always have the same outcome, no matter whether they derive from original b, d, g or mb, nd, ŋg:
    • dôl (head) > *i-dhôl (the head) | regularly *i-ndôl (cf. Fanuidhol, NDOL-)
    • bas (bread) > i-vas (the bread) | regularly i-mbas (ÑGUR-)
    • gurth (death) > *i'urth (the death) | regularly *i-ngurth (ÑGUR-)
    • ...

Analogical instead of archaic past tenses
The Etymologies' N. had a great amount of later analogical past tense forms and though past tense formation in later S. appears to be largely different there are still some analogical forms which should very likely be preferrable in Gondorian Sindarin:
    • gala- (grow) > angol (grew, *añgāle) | regular aul (agāle) [all PE17:131]
But maybe the habit of creating weak past tenses from strong verbs attested in N. can still be used in S., thus:
    • dag- (slay) > degant (slew) | regular N. danc, S. aðag, aðanc [LR:375, VT45:37, PE17:131]

What can be said with certainty about past tenses in Gondorian Sindarin is that we have to be careful when we append personal suffixes to the impersonal/3.sg. form, since the frequent consonantal clusters -nt, -nc, -mp do not behave as in regular Sindarin but change the stop to a spirant medially (cf. nþ, ŋχ, mφ, lþ above). Thus we find changes of this sort:

covant (met) > *covanthen (I met) | cf. regular mae govannen
adhanc (slew) > *adhanchen (I slew) | cf. regular dangen [dɑŋ:ɛn]
agramp (talked) > *agramfen (I talked) | regular *agrammen (in fact the form was struck out and replaced by agarfant)

• • •

3. Vocabulary

In Tolkien's writings there appear several word that are only found in the Gondorian variety of Sindarin or that are in this dialect used in a different way. Below follows an alphabetical list of what I believe and hope to be all words known to us (made by help of Hiswelókë's Sindarin dictionary):

canath [ˈkɑnɑθ] n. quarter | Silver coin used in Gondor, fourth part of a 'mirian' [XII:45]
canthui [ˈkɑnθʊi] adj. fourth | regular *cannui [VT41:28]
daur [ˈdɑʊr] n. league | About 3 miles. Normally a noun stop, pause, used as measure because in marches the Dúnedain usually made a brief halt after this distance [UT, Three, I, n.9]
dírnaith [ˈdiːrnɑiθ] n. man-spearhead | "a wedge-formation, launched over a short distance against an enemy massing but not yet arrayed, or against a defensive formation on open ground" [UT, Three, I, n.16]
enchui [ˈɛŋχʊi] adj. sixth | regular *engui [ˈɛŋ:ʊi] [VT41:27]
erui [ˈɛrʊi] adj. first | Elvish: single, alone [TI:312; XI:436; VT42:10]
mirian [ˈmiriɑn] n. a certain coin [XII:45]
rath [rɑθ] n. street | Used of the streets of Minas Tirith nearly all of which were on an incline. Normally maybe a noun climb, cf. Andrath [UT, The Elessar, n.16]
thangail [ˈθɑŋgɑil] n. shield-fence | thand-cail, battle formation of the Dúnedain: "a shield-wall of two serried ranks that could be bent back at either end if outflanked, until at need it became a closed ring"[UT, Three, I, n. 16]
tolthui [tɔʟθʊi] adj. eighth | regular *tollui [VT41:27]

Due to the differences in phonology explained above some vocabulary has to be changed in order to represent a usual Gondorian form:
*Abonthen [ɑˈbɔnθɛn] pl. *Ebenthin [ɛˈbɛnθin] adj./n. afterborn, man | regular Abonnen pl. Ebœnnin [WJ:387]
antha- [ˈɑnθɑ] v. to give| regular anha-, anna- [LR:348, PE17:93]
*atlantha- [ɑtˈʟɑnθɑ] v. to slope, slant| regular atlanna- [LR:390]
*bancha- [bɑŋχɑ] v. *to trade | regular banga- [bɑŋ:ɑ] [LR:372]
possibly *belthas [bɛlθɑs] n. bodily strength | regular bellas might be from *beltass- or *beldass- [LR:352]
*canthas [ˈkɑnθɑs] n. shaping| regular #cannas [WJ:192,206]
*centhan [ˈkɛnθɑn] n. potter| regular cennan [LR:390]
*covanthen [kɔˈvɑnθɛn] pp. met| regular covannen [LotR:I, Let., PE17]
*danchen [ˈdɑŋχɛn] pl. *denchin [ˈdɛŋχin] pp. slain | regular dangen [ˈdɑŋ:ɛn] pl. dengin [ˈdɛŋ:in] [LR:275, Sil]
*dantha- [ˈdɑnθɑ] v. to fall| regular danna- [PE17:62]. Past participle 'fallen' perhaps *danthen, since N. dant- has dannen [LR:354]
doltha- [dɔʟθɑ] v. to conceal | from N., regular S. rather *dolla- [LR:355]
*edontha- [ɛdˈɔnθɑ] v. to beget| regular edonna- [LR:379]
*enthas [ˈɛnθɑs] prep. there| regular ennas [SD:129-31]. But cf. note on the King's Letter at nþ,... above)
*gobenthas [gɔbˈɛnθɑs] n. history| regular gobennas [LR:366]
*gobenthathren [gɔbˈɛnθɑθrɛn] adj. historical| regular gobennathren [gɔbˈɛn̥:ɑθrɛn] [LR:366]
*gwantha- [ˈgwɑnθɑ] v. to depart, die | regular gwanna- [LotR:II]
haltha- [hɑʟθɑ] v. to screen | from N., regular S. rather *halla- [LR:286]
heltha- [hɛlθɑ] v. to strip | from N., regular S. rather *hella- [LR:386]
*hamfa- [hɑmφɑ] v. to clothe | regular hamma- [LR:363, VT45:21]
*hamfad [hɑmφɑd] ger./n. clothing | regular hammad [LR:363]
*limfid- [ʟimφid] v. to moisten | regular *limmid-, from N. lhimmid- [LR:369]
malthen [mɑʟθɛn] adj. golden | regular mallen [LR:386]
malthorn [mɑʟθɔrn] n. golden tree of Lórien | regular mallorn [LotR:II, Sil., VT41:27]
possibly *mintha- [ˈminθɑ] v. to enter | regular minna- may derive from *minta- [LR:397]
*nimfid- [nimφid] v. to whiten | regular nimmid- [LR:378]
*ontha- [ˈɔnθɑ] v. to beget | regular #onna-, cf. abonnen, edonna- [WJ:387, LR:379]. Past participle *onthen from regular #onnen.
*pantha- [ˈpɑnθɑ] v. to open, enlarge| regular panna- [ LR:380]
pelthaes [ˈpɛlθɑɛs] n. pivot | from N., regular S. maybe rather *pellaes [LR:380,390]
*penthas [ˈpɛnθɑs] n. history, historical account| regular pennas- [ LR:366, WJ:192,206]
*prestanthen [ˈprɛstɑnθɛn] pp. affected, mutated| regular prestannen [ LR:380]
*prestantheth [ˈprɛstɑnθɛθ] n. affection of vowels, mutation| regular prestanneth [ LR:380]
*soganthen [ˈsɔgɑnθɛn] pp. drunk| regular sogannen [ LR:3880]
*suilantha- [ˈsʊiʟɑnθɑ] v. to greet, give greetings | regular suilanna- [ SD:129-31]
*suilanthad [ˈsʊiʟɑnθɑd] ger./n. greeting | regular suilannad [ SD:129-31]
*tanchada- [ˈtɑŋχɑdɑ] v. to make firm, confirm, establish | regular tangada- [ˈtɑŋ:ɑdɑ] [LR:389]
*thintha- [ˈθinθɑ] v. to fade, to grow towards evening | regular thinna- [LR:392]
*thinthas [ˈθinθɑs] n. "shortness" (diacritic indicating short vowels) | regular thinnas [LR:388]
possibly *tintha- [ˈtinθɑ] v. to glint | regular tinna- might be from *tinta- or *tinna-/*tinda-[LR:393]
toltha- [tɔʟθɑ] v. to fetch, summon, make come | from N., regular S. rather *tolla- [LR:395]