Across:
1 It’s slightly ridiculous (BIT OF NONSENSE) coming out of Limerick (limerick poem = BIT OF NONSENSE),
10 Men fail (men fail = INFLAME) badly (= anagram indicator) to provoke trouble (INFLAME),
11 On the radio (= homophone indicator) switch (switch = ‘knob’ = ‘nob’ = N-OB-) over – most of 29 across (most of ‘airs’ = -AIR-) is taking independence (-I) (NAIROBI) in African capital (capital of Kenya = NAIROBI),
12 Served up (= reversal indicator) some spaghetti meals (some ‘spaghetti meals’ = ti me = EMIT) to give out (EMIT),
13 Blown away (SLAIN) by small (S-) American city (Los Angeles = -LA-) that’s popular (-IN) (SLAIN),
15 Knocks back (= reversal indicator) sample of alcohol socialising (sample of ‘alcohol socialising’ = ol so = OSLO) in European capital (OSLO)
17 Easy going without saying (‘easy going’ without ‘saying’ = eog = EGO) one needs this to recognise one’s own importance (EGO),
19 Local crazy guy (NUT-) promotes academic research (Royal Irish Academy = -RIA) (NUTRIA) of river rat (NUTRIA),
21 A (-A) large (-L-) vault (leap = PAEL-) blown up (= reversal indicator) (PAELLA) in Spanish restaurant (PAELLA),
22 Can’t figure out why (MYSTERY) my tyres (my tyres = MYSTERY) burst (= anagram indicator),
23 If the other crossword (Simplex) isn’t finished (x) (Simplex’ without ‘x’ = SIMPLE) it’s not difficult to see why (SIMPLE),
25 Nothing (O-) modern (new = -NE W-) from a (-A-) yard (-Y) (ONE WAY) resembles a mirror (ONE-WAY mirror),
27 Took in (ATE) what’s packed away in delicatessen (what’s packed away in ‘delicatessen’ = ATE),
29 Broadcasts (AIRS) lie from Israeli (‘lie’ from ‘Israeli’ = srai = AIRS),
30 Ladies’ men missing Isle? (‘ladies men’ missing ‘Isle’ = admen = AMEND) Correct! (AMEND),
31 Woman leaves Jamestown (‘woman’ leaves ‘Jamestown’ = jest = JEST) with kid (JEST),
34 Note (N.B. = -BN-) that is (i.e. = -EI-) carried back (= reversal indicator) concealed by Bess (L-IZ) (LEIBNIZ), a German mathematician (LEIBNIZ),
35 Pierce again (pierce/go in again = RE-ENTER) is writing (from the 3Rs = R-) and finishing the (finishing ‘the’ = -E-) record (-ENTER) (RE-ENTER),
36 Divide sandwich (divide ‘sandwich’ = S AND) flan (PIE-) with cream topping (‘cream’ topping = -C-), surround it with nibbles (bites = BIT -ES) (BITS AND PIECES) and an assortment of stuff (BITS AND PIECES).
Down:
2 One (I-) new (-N-) film (flick) cut (k) (‘flick’ without ‘k’ = - FLIC-) by projectionist at the centre (‘projectionist’ at the centre = -T) (INFLICT) to cause trouble (INFLICT),
3 Fragment of the Chekhov allegory (fragment of the ‘Chekhov allegory’ = ov al = OVAL) found in the ground in Australia (OVAL),
4 Elder statesmen to get rid of the smart set (‘elder statesmen’ to get rid of the ‘smart set’ = eldeen = NEEDLE) for Spike (NEEDLE),
5 Sister (NUN-) from island (-I-) taken in by company (Co = -C-O) (NUNCIO) ambassador (NUNCIO),
6 Relative drops rate (‘relative’ drops ‘rate’ = live = EVIL) for wicked type rotten to the core (EVIL),
7 Relates to the marrying (SPOUSAL) of small (S-) flower (flower/river Po = -PO-) from America (-USA-) with lilies primarily (‘lilies’ primarily = -L) (SPOUSAL),
8 Inability to eat starters (‘inability to eat’ starters = -ITE-) surrounded by rib (bone = B- ONE) and escargots? (snails = -S NAILS) (BITE ONE’S NAILS) Chew finger food! (BITE ONE’S NAILS),
9 Shrouded in secrecy, for example (BIT OF A MYSTERY), little (BIT) duck (O-) fat (fat) mostly (t) (‘fat’ without ‘t’ = -F A) added to processed meat (MYSTERY meat) (BIT OF A MYSTERY),
14 Does that stir it up (AGITATE) for lead actor (lead ‘actor’ = A-) in theatre (Gate Theatre = -G-ATE) hiding a fair amount of (half of) irritation? (half of ‘itch’ = -IT-) (AGITATE) (AGITATE),
16 Papers (ID papers = DI-) reviewed (= reversal indicator) by Mike (-M-) only half (‘only’ half = -LY) (DIMLY) seen but not in the best light (DIMLY),
18 Refuse a request (SAY NO) to do the opposite to what’s in 20 down (SAY NO is the opposite of ‘aye’),
20 Reply to captain (AYE) discovered in Jan Mayen Island (discovered in ‘Jan Mayen Island’ = AYE),
21 Expert (PRO) is irate leaving Pretoria (‘irate’ leaving ‘Pretoria’ = pro = PRO),
24 Drink (MARTINI) to songbird (MARTIN- / swallow family) on single (-I) (MARTINI),
26 Come to terms with (WRESTLE with) job in Ring (WRESTLE),
27 River (AMAZON) in Oman (Oman = AM-ON) travelling (= anagram indicator) around a (-A-) zone (-Z-) (AMAZON),
28 Old man (partner) backing off (r) (“partner’ without ‘r’ = partne), retiring (= reversal indicator) (partne = ENTRAP) to corner (ENTRAP),
32 Paper (Sun = -NUS) round (O-) brings up (= reversal indicator) (ONUS) the issue of responsibility (ONUS),
33 Some cliché repeated (some ‘cliché repeated’ = he re = HERE) in this place (HERE).