Across:
1 Opens 14 across (opens 'coffee breaks' = COFFEE) to drink (COFFEE),
4 Spike (SPUR-) has debts? (IOUs = -IOUS) (SPURIOUS) Apparently, but they’re not genuine! (SPURIOUS),
9 One half (MOIETY) of Ireland (.ie = -IE-) consumed by short witty remark (mot = MO-T-) with bawdy ending (‘bawdY’ ending = -Y) (MOIETY),
10 Looks after (minds = MIND’S) one of the viewers (EYE) (MIND’S EYE) with an imagination (MIND’S EYE),
12 Paying attention to the numbers, steps taken (BOSSA NOVA dance) by one running the business (BOSS-) for a (-A) bright star (NOVA) (BOSSA NOVA),
13 Encourage (EGG ON) suits to leave suggestion (‘suits’ to leave ‘suggestion’ = ggeon = EGG ON),
14 Pauses doing a job (COFFEE BREAKS) for firm (CO-) ahead of floatation (ahead of ‘Flotation’ = -F-) for payment (-FEE) and falls to pieces (BREAKS) (COFFEE BREAKS),
18 Those in the lounge can hold drink (COFFEE TABLES) with 1 across (‘coffee’ = COFFEE) and 19 down (‘tables’ = TABLES) (COFFEE TABLES),
21 A friend in Lyon (Lyon/French ‘friend’ = ‘ami’ = AMI-) on leave (leave = -GO) (AMIGO) with a friend in Barcelona (Spanish ‘friend’ = AMIGO),
22 One of the key men (LOCKSMITH) provides security (LOCKS-) at the state’s college (Massachusetts Institute of Technology = -MIT-) hospital (-H) (LOCKSMITH),
24 Paid tribute to (LIONISED) rugby player (LION-) on touring (= anagram indicator) side (side = -ISED) (LIONISED),
25 Lament (BEWAIL) produced by lawyer (BL = B-L) over rising (= reverse indicator) astonishment (awe = -EWA-) at Independence (-I-) (BEWAIL),
26 Those from the granite city (The Granite City = Aberdeen) presumably (SCOTTISH) producing alternative (= anagram indicator) to schist (to schist = SCOTTISH),
27 Snaps (BREAKS) baker’s (bakers) crackers (= anagram indicator) (bakers = BREAKS).
Down:
1 It's in response (COMEBACK) to what you might make after retiring (make a COMEBACK),
2 Mark (FAIL-) is employed in a bank (-SAFE) (FAIL-SAFE) and is guaranteed to work (FAIL-SAFE),
3 Over and above (EXTRA) former (EX-) beach in Ireland (Irish for ‘beach’ = trá = -TRA) (EXTRA),
5 Soldier (PRIVATE) landing on Banna Strand (BEACH) (PRIVATE BEACH) – a sandy place that’s not open to the public (PRIVATE BEACH),
6 One of Daisy’s relatives (RUDBECKIA) is impolite (rude) missing the final (‘rude’ without ‘e’ = RUD-) half of Beckett’s (half of ‘BECKetts’ = -BECK-) first-class (AI) review (= reversal indicator) (AI = -IA) (RUDBECKIA)
7 Turns up (= reverse indicator), for example (e.g. = -GE), to study (den = -N ED-) at Oxford (O-) (ON EDGE), a bundle of nerves (ON EDGE),
8 Generalise without real (‘generalise’ without ‘real’ = genise = SEEING) viewing (SEEING),
11 Suspicion (DOUBTFULNESS) this is open to debate (DOUBTFUL-) on four points, one of them repeated (four compass points = north east south south = -NESS) (DOUBTFULNESS),
15 Comes in to (comes in to) shift (= anagram indicator) (comes into = ECONOMIST) an expert on financial management (ECONOMIST),
16 Final offers (ULTIMATA) from University (University of Limerick = UL-) – the one teaching American students (MIT) returning (= reverse indicator) (MIT = -TIM-) to the middle of Qatar (the middle of ‘qATAr’ = -ATA) (ULTIMATA),
17 Paves the way (ASPHALTS) to halt Spa’s (halt Spas) work (= anagram indicator) (halt Spas = ASPHALTS),
19 Myths (tales = TA-LES) about open bar (open ‘Bar ‘= -B-) (TABLES) used by the mathematicians (TABLES),
20 Order (-O-) in mink (mink) dress (= anagram indicator) (mink = KIM-N-) with order (-O) (KIMONO) for robe (KIMONO),
23 Told off old master (‘told’ off ‘old master’ = maser = SMEAR) producing false accusation (SMEAR).