I got bogged down in the top half of this puzzle, particularly the NE where Casals was a piece of GK too far for me, resulting in a long trawl of Cawalt, Casamb, Catang, Cagalo... the possibilities are almost endless if classical musicians don't have to be your forte and you have foolishly not nailed down the answer to 8d. I certainly experienced the phenomenon of the MER several times during this puzzle, but there were also some straight up brilliant clues, let me single out the unlikely-seeming containment in 14dn, the fact that 15ac so deceptively screams out "anagram", and my COD, the only actual straight-up anagram of the entire puzzle, 2dn. Very well played to the setter for serving up a proper Friday toughie, that I hope I will not discover in the morning took Mohn under 4 minutes to crack!
ACROSS
1 Iberian: what brought about a state of agitation for him? (8)
HISPANIC - in a state of agitation due to HIS PANIC
5 A short dance written by composer, primarily for cellist (6)
CASALS - A SALS{a} written by C{omposer}. Pablo, the pre-eminent cellist of the first half of the 20th century
10 No-win situation fair, on reflection, in report (9)
STALEMATE - reversed MELA [(Hindu) fair] in STATE [report]. Gotta say I thought "mela" the kind of vocabulary that would be more suited to the Monthly Club Special or Listener, but perhaps it's just me that never heard of one before...
11 Ring doughnut at last comes in for my sweet (5)
PETAL - PEAL [ring] that {doughnu}T comes into. A term of endearment
12 Very big self-obsession, Georgia (4)
MEGA - ME [self-obsession?] plus GA (the American state). Obviously "me" is a big part of "self-obsession", I wasn't necessarily convinced that they are completely substitutable for each other...
13 Chap after party lapping up cheers — some function! (9)
COTANGENT - GENT after CON(servatives) "lapping up" TA [cheers]
15 Current cycle trail, scintillating (10)
IRIDESCENT - I RIDE SCENT [current | cycle | trail] - hands up if your brain too was desperate to anagram this into "electricity"...
17 Native American doctrine unfinished (4)
CREE - CREE{d}, FOI
19 Company was gloating (4)
CREW - double def. As in the past tense of "crow", SOI
20 On having cracked puzzle, enough to demonstrate my point (3,7)
FOR EXAMPLE - RE [on], having "cracked" FOX [puzzle], + AMPLE [enough]
22 Critic: one choosing “Dumbo”, perhaps? (3-6)
NIT-PICKER - a dumbo is a twit is a nit, so if you choose it you're a nit-picker
24 Handle towards the rear on back of latch (4)
HAFT - AFT [towards the rear] on {latc}H
26 Eastern European going west? Get away! (5)
ELOPE - reversed E POLE
27 Use of weapon when body enters fray (5,4)
RIFLE SHOT - FLESH "enters" RIOT
28 Flower attached to tail of giant guinea pig (6)
TASTER - ASTER attached to {gian}T
29 Holy work restricting perversion of rites (8)
PRIESTLY - PLY "restricting" (RITES*)
DOWN
1 Crowd present (4)
HOST - double def, "present" as in "emcee", not "gift"
2 Player's brief decision targets game (5,10)
STAGE DIRECTIONS - (DECISION TARGETS*). Hats off to "game" as a surreptitious anagrind
3 Maintain senior was usually around? (8)
AVERAGED - AVER AGED [maintain | senior]. If "the temperature averaged 30", it was usually around 30...
4 Biblical character represents Adam oddly, and Charlie (5)
ISAAC - IS [represents] + A{d}A{m} + C
6 Porter maybe carrying small drink up mountain (6)
ALPINE - ALE [porter, maybe] "carrying" reversed NIP. Mountain in the adjectival sense here
7 Where boater may go down instantly? (2,3,4,2,1,3)
AT THE DROP OF A HAT - boater being a type of hat
8 Sprayed with liquid in second: dashed about? (10)
SPLATTERED - LATTER [second], with SPED [dashed] "about" that. This took ages as I got stuck on the S being the second and couldn't work out which of PLATTERED or PLUTTERED was more likely to mean "dashed"
9 Period ends this time in prison? (8)
SENTENCE - double def
14 Throw candleholder into mire (10)
DISCONCERT - SCONCE into DIRT
16 China — country gutted about Elvis, say? (8)
CROCKERY - C{ountr}Y "about" ROCKER
18 Fabric in green, pure and simple (8)
CASHMERE - CASH [green, as in folding stuff or lolly] + MERE [pure and simple]
21 Galley providing portion of lamb, I remember (6)
BIREME - hidden in {lam}B I REME{mber}
23 Direct favour initially ignored (5)
REFER - {p}REFER
25 Those last in races at sea may remain behind (4)
STAY - {race}S {a}T {se}A {ma}Y