Solution to 13A has been deliberately left unsolved and is to be answered only by a non-regular / novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
Open for anyone to answer, if not solved by 1 PM.
ACROSS
1 What model might say she's doing is impressive (8) IMPOSING {I'M POSING}
5 Most thrilled, about to marry in European country (6) SWEDEN {S{WED}ENt}
12 Criticism by newly-wed crushes groom's heart, terribly sad (9) BROADSIDE {BR{grOom}{SAD*}IDE}
13 Batter in decline after gaining pounds (5) F?A?L (Addendum - FLAIL {F{L}AIL} - See comments)
14 Funny scene about a meeting to raise the spirits (6) SEANCE {SE{A}NCE*}
15 Connects parts to conserve power (7) SPLICES {S{P}LICES}
18 Muffins, tea? Deli sandwiches, alternatively (7) INSTEAD [T]
20 Supporting retired man in difficulty (6) BEHIND {B{HE<=}IND}
22 Many crave for hidden treasure (5) CACHE {C}{ACHE}
24 Knocking back gin, miss cuddling lover finally mated (9) PARTNERED {TRAP<=}{NE{l..eR}ED}
25 Promiscuous actor chasing lady in set is millionaire (9) PLUTOCRAT {ACTOR}*<=>{P{L}UT}
26 One with snare crossing large creek (5) INLET {1}{N{L}ET}
27 Root may be run out, leaving Australia's captain excited (6) EMBRYO {MaY+BE+RO}*
28 Groupie in rave taking off posh gown (8) PEIGNOIR {GROuPIE+IN}*
DOWN
2 Glib Spanish man going around with society lady providing financial support (9) PATRONESS {PAT}{SENOR<=}{S}
3 What to do when national anthem's played at event? Behave formally (5,2,8) STAND ON CEREMONY [C&DD]
4 Include new species of atom (7) NUCLIDE*
6 Fantasy of fling with hunk is exciting (7,8) WISHFUL THINKING {FLING+WITH+HUNK+IS}* Semi&lit
7 Play diamond ace to secure slam (5) DRAMA {D}{RAM}{A}
8 Taunts son? That's uncalled-for (8) NEEDLESS {NEEDLES}{S}
9 Kisses girl on drive back (6) GREETS {G}|{STEER<=}
16 Tenor in control, a fantastic voice (9) CONTRALTO {T} in {CONTROL+A}*
17 Criticize film about the French student (8) DISCIPLE {DIS}{PIC<=}{LE}
19 Take off in record-breaking run (6) DEPART {D{EP}ART}
20 Better U-shaped glass tube (7) BURETTE*
23 Bit of cold drink with bit of booze (5) CRUMB {C}{RUM}{Bo..e}
Reference List
Old = O, Pounds = L, Power = P, Many = C, Lady = L, Run Out = RO, Posh = U, Glib = PAT, Society = S, Diamond = D, Ace = A, Son = S, Girl = G, Tenor = T, Criticise = DIS, The in French = LE, Record = EP(Extended Play), English = E, Italian Vermouth = IT, Cold = C