Across:
1 Criminal (= anagram indicator) bosses (bosses = OBSESS) think it through relentlessly (OBSESS),
4 Kept an eye on (OBSERVED) flounder (= anagram indicator) over beds (over beds = OBSERVED),
9 Blew the whistle on (TOOTED) writer (-ED) after (= positional indicator) getting signal (TOOT-) (TOOTED),
10 Devour (-EAT-) in pamphlet (flyer = FLY-ER) (FLY-EATER) produced by one of those responsible for The Web (FLY-EATER),
12 Playing (= anagram indicator) tune in car (tune in car = UNCERTAIN) is risky (UNCERTAIN),
13 Environmentally friendly (GREEN) roads out of rose garden (‘roads’ out of ‘rose garden’= egren = GREEN),
14 God (SUPREME BEING) – who is that upstairs? (SUPREME BEING),
18 For the present time (BIRTHDAY), Madeira, for one, (Madeira CAKE) (BIRTHDAY CAKE) is popular for an annual blow-out? (BIRTHDAY CAKE),
21 Caught (C-) broadcast (-AIR-) from old (-O) (CAIRO) African city (CAIRO),
22 Refuse to drop off (KEEP AWAKE) stock (KEEP) for The Dead (a wake = AWAKE) (KEEP AWAKE),
24 Sherry (APERITIF) turns up (= reversal indicator) in good shape (fit = -TIF) from Ireland (IRE = -ERI-) for public address (public address = PA = AP-) (APERITIF),
25 Praetorian guard takes off, departing (‘Praetorian guard’ takes off ‘departing’ = roauar = AURORA) for light show (AURORA),
26 Sorted out (RESOLVED) local crack (RESOLVE-) and diamonds (-D) (RESOLVED),
27 In retrospect (= reversal indicator), writer (ed = D-E) goes around eatery (café = -EFAC-) (DEFACE) with Sully (sully/damage = DEFACE).
Down:
1 Explosion of emotion (OUTBURST) seen in Ring (bout) needs no introduction (b) (‘bout’ without ‘b’ = OUT-) to Pop (-BURST) (OUTBURST),
2 Winter coat (SNOW-) for Trump (trump/surpass = CAP-) bearing (bearing south = -S) (SNOWCAPS) material from the top of The Aspen Mountains, for instance (SNOWCAPS),
3 Drive (STEER) out of wild (= anagram indicator) trees (trees = STEER),
5 The doctrine of egalitarianism (BALANCE-) from Dublin (-D) Congress? (congress/senate = DIET) (BALANCED DIET) If you’re a consumer of this, it won’t weigh much on you! (BALANCED DIET),
6 Crisis (EMERGENCY) for most of (n) the workers (‘men’ without ‘n’ = -ME-) in New (= anagram indicator) Regency (Regency = E-RGENCY) (EMERGENCY),
7 Rejects (VETOES) a fair amount (half of) of the meat (veal) (half of ‘VEal’ = VE-) on the little piggies (-TOES) (VETOES),
8 Throwing down the gauntlet (DARING) to relative (DA-) in Waterford (-RING) (DARING),
11 Sounds like (= homophone indicator) taste of wine (‘palate’ = ‘PALETTE’) is sharp (KNIFE) (PALETTE KNIFE) and could strip paint (PALETTE KNIFE),
15 The leader’s opinion (EDITORIAL), aside from the letter writers (EDITORIAL aside/at one side of “Letters to the Editor”),
16 Short (e), legal action (‘case’ without ‘e’ = CAS-) upsets (= reversal indicator) a (-A-) lady selling cosmetics (Avon lady = Avon = -NOVA) (CASANOVA) to lover boy (CASANOVA),
17 Take a girl out (D-ATE), taking in final performance (final ‘performancE’ = -E-) on stage (-LEG-) (DELEGATE) of The Mission (DELEGATE),
19 Community (European Community = EC-) shelter (-LAIR) (ECLAIR) offering French cake (ÉCLAIR),
20 Cried (cried = CIDER-) out (= anagram indicator) at school (-S) (CIDERS) for apple drinks (CIDERS),
23 Entertain (AMUSE) a (A-) creative influence (-MUSE) (AMUSE).