Across:
1 Band Aid (SPEAKER) calls (-PHONES) (SPEAKERPHONES) and presumably these sound types pick up on what's been openly said by everyone (SPEAKERPHONES),
10 Wise (POLITIC) polemicists ignoring mess (‘polemicists’ ignoring ‘mess’ = policit = POLITIC),
11 Posted (posted) problem (= anagram indicator) (posted = DES-TOP) over the weekend (‘weeK’ end = -K-) (DESKTOP) from computer (DESKTOP computer),
12 State (AVOW) of first aid (first ‘Aid’ = A-) order (-O-) found in vehicle (VW Volkswagen = -V-W) (AVOW),
13 All those starting today (SPEAK on all sides of today’s grid) sound off (SPEAK),
15 Field of expertise (AREA) in The Far East (in ‘the fAR EAst’ = AREA),
17 Make a mistake (ERR) getting back (= reverse indicator) into arrears (into ‘aRREars’ = rre = ERR),
19 Isn’t (isn’t) worried (= anagram indicator) (isn’t = INS-T) about Clare (-EC-) throwing up (= reverse indicator) (CE = -EC-) (INSECT) with bug (INSECT),
21 William (BILLY-) – the first from Orange (‘Orange’ first = -O) (BILLY-O) to demonstrate it with great gusto (BILLY-O),
22 Henry (H-) and Ray (-X- ray) in Genoa (Genoa) playing (= anagram indicator) (Genoa = -E-AGON) (HEXAGON) six-a-side? (HEXAGON),
23 Brief (l) officer (‘general’ without ‘l’ = GENERA) in the ranks of the family divisions? Naturally! (ranks/family divisions = GENERA = plural of genus),
25 Boutiques losing out (‘boutiques’ losing ‘out’ = biques = BISQUE) to something fishy that appeals to consumers (BISQUE),
27 Bile from Belgium (‘bile’ from ‘Belgium’ = gum = GUM) is something to chew over (GUM),
29 Detached (LONE) from the extremes of revolutionary (= reverse indicator) environmental control (the extremes of revolutionary ‘ENvironmental contrOL’ = enol = LONE),
30 Stand up (stand-up COMIC) for dandy? (Dandy COMIC),
31 Lamb (lamb) stew (= anagram indicator) (lamb = BALM) can be soothing on the lips (BALM).
34 Tree (CATALPA tree) in California (CA = C-A) covering area (-A-) on top of Twin (on top of ‘Twin’ = -T-) Peak? (-ALP-) (CATALPA),
35 Rebuke (CHASTEN) for 100 (Roman 100 = C-) from Rush (-HASTEN) (CHASTEN),
36 Don’t follow advice from perjurer (SPEAK THE TRUTH) to quote what’s Gospel (SPEAK THE TRUTH).
Down:
2 Those presumably interested in 4 down (POWS interested in 'escape' = P-OWS) admit being sick (being sick = -ILL-) (PILLOWS) of those providing support for the heads retiring (PILLOWS),
3 At the beginning and the end of Arabian Nights (at the beginning and the end of ‘ARabian nighTS’ = ARTS) to a degree (ARTS degree),
4 Get away (ESCAPE) with case to East Indies (case to ‘East indieS’ = ES-) headland (-CAPE) (ESCAPE),
5 Overheard (= homophone indicator) couple (‘pair’ = ‘pear’ = PE-AR) touring Donegal (-DL-) (PEDLAR) going from place to place selling items (PEDLAR),
6 Get rid of (OUST) heroes thrown out of Storehouse (‘heroes’ thrown out of ‘Storehouse’ = tous = OUST),
7 Entrance (entrance/charm = ENTHRAL) to hotel (-H-) on square (-T- square) in Ulster port (Larne) experiencing upturn? (= reverse indicator) (Larne = EN-RAL) (ENTHRAL),
8 Presumably, someone called time on this service that’s no longer available (SPEAKING CLOCK) – I used to ring it to get The Times? (SPEAKING CLOCK),
9 State (SPEAK) of new tops (‘Of New’ tops = ON-) and denims (denims)? Awful (= anagram indicator) (denims = -E’S MIND) (SPEAK ONE’S MIND) to be frank! (SPEAK ONE’S MIND),
14 Made a mistake publishing (ERRATUM) maturer (maturer) novel (= anagram indicator) (maturer = ERRATUM),
16 Shady type (OCHRE) of leader on (leader ‘On’ = O-) the run (run in cricket = -R-) taken in by revolutionary (Che = -CH-E) (OCHRE),
18 Those driven types (MINIS) immersed in feminism (immersed in ‘feMINISm’ = MINIS),
20 Segment of schoolteachers (segment of ‘schoolTEAchers’ = TEA) make a meal of it (TEA),
21 Short cut perhaps (a BOB hair cut) leads to back of beyond (leads to ‘Back Of Beyond’ = BOB),
24 It’s relentless (NON-STOP) operating (-ON-) after (= position indicator) mid-morning (mid ‘morNing’ = N-) break (-STOP) (NON-STOP),
26 Neighbourhood (quarter) isn’t finished (r) (‘quarter’ without ‘r’ = QUARTE-) on time (-T) (QUARTET) for group going through the numbers (QUARTET),
27 George (G-), Oscar (-O-), Kay (-K-) and Arthur (-ART) (GO-KART) driven to the limits by a boy-racer (GO-KART),
28 Make a bags of it taking on The Reds (miss the snooker ball = MISCUE) I heard (= homophone indicator) to avoid (‘miss’ = ‘mis’ = MIS-) stick? (cue from snooker hall = -CUE) (MISCUE),
32 Mount Blanc (alp) rising (= reverse indicator) (alp = PL-A) over foundation of gorge (foundation of ‘gorgE’ = -E-) (PLEA) or that’s the claim (PLEA),
33 Similar to what you need for 21 down (HAIR needed for ‘bob’ hairstyle), it grows on one (HAIR).