Not too tricky at this station, arriving fully parsed in 20.19, but as you may infer from my ramblings below, there are quite a few bits where the general knowledge may not be all that general. I rather liked the clean surfaces of 21 and 23, and I don’t think there’s a dud clue anywhere. But I believe we have the first appearance of the rather ugly term for a Political Advisor, which would previously have been clued perforce as Signal Passed At Danger, and as far as I can see, the grammatical term at 1a is making its first appearance too. For that and the Elizabethan playwright at 27 some inspired guesswork might be needed by some of this order, but I don’t think they’re impossible or unfair.
Along with my musings, I have reproduced the clues, definitions and SOLUTIONS.
Across
1 Perhaps May’s second day, all very endless and black (5,4)
MODAL VERB Right. Pay attention, class, because for once, you won’t have learned this bit of grammar in Mr Jarry’s Latin lessons. “A modal verb is a type of verb that is used to indicate modality – that is: likelihood, ability, permission, request, capacity, suggestions, order, obligation, or advice. Modal verbs always accompany the base (infinitive) form of another verb having semantic content. In English, the modal verbs commonly used are can, could, may [without a capital!], might, shall, should, will, would, and must.” Or you can just follow the wordplay and hope for the best. Second is MO, plus D(ay), plus AL(l) and VER(y) “endless”, plus B(lack)
6 Old heating unit bust after time (5)
THERM Which I thought we still used, but apparently one therm is equal to about 105.5 megajoules, 25200 kilocalories, or 29.3 kilowatt-hours, which looks like a lot in any old or new units. T(ime) goes before HERM, which is (or you hope it is) a bust of some kind: “a head or bust (originally of Hermes) on a square base, often double-faced”.
9 Friend’s gone — I’m back inside (5)
AMIGO Rather more accessible: AGO for gone (in the past) with I’M reversed within, like it says.
10 Risk damage when drilling patent bucket? (9)
OVERTRAIN Which must be drilling as in square bashing. Patent gives OVERT and the RAIN buckets down.
11 Bogey fault west of Paddington? (7)
BUGBEAR Fault gives BUG, and Paddington is the quintessential BEAR. From Peru.
12 Annexe about to run into chalk ground (7)
WHITING Finely ground chalk can be used for various whitening applications. Annexe is WING (of a building) and run into gives you the HIT to put inside
13 Song at cricket ground such as Worcester and Oxford? (5,9)
LORDS SPIRITUAL are the 26 (of 42) Bishops of the CofE who are entitled to sit in the House of Lords. Five are Canterbury+, York+, London+, Durham+, and Winchester+, plus a selection of the rest, currently including those of Oxford+ and Worcester+, though they are only so entitled by seniority, the length of time they serve, unless they’re women, in which case they take precedence. To appoint them to this grid, imagine an African-American song such as Swing Low being sung at the Home of Cricket instead of Sweet Caroline or the dreary Don’t Take Me Home.
17 One — and he spends freely — showing this? (4-10)
OPEN-HANDEDNESS Sort of &lit. An anagram (freely) of ONE AND HE SPENDS. For once, one is not just I
21 Post Office note about label showing cost of carriage (7)
PORTAGE P(ost) O(ffice) plus the first random note of the day E, surrounding TAG for label. [On edit: as others have pointed out, the note is the sol fa RE, otherwise the R is missing]
23 Gradually destroy fuel element in reactor’s heart (7)
CORRODE Fuel element ROD, and reactor’s heart to put it in CORE.
25 Trouble holding double plastic bomb (9)
DOODLEBUG The V1 flying bomb of WWII. Trouble is DOG, and an anagram (plastic) of DOUBLE is held therein.
26 Best garden party? (5)
OUTDO Party is a DO, and one in the garden would be OUT(side).
27 Society dramatist of Elizabethan times in the manner of Fox (5)
SLYLY S(ociety) plus John LYLY, well known (?) for his plays Campaspe and Mother Bomble. We are not necessarily helped by the fact that Lyly is only one way in which John spelled his surname, given that our answer can also be rendered as SLILY
28 Happy to direct how refugees are often accommodated (9)
CONTENTED CON for direct (as in “you have the con(n) Mr Sulu”) plus well, yes, how refugees are often accommodated, TENTED
Down
1 Stupid American encountered outside a dance (8)
MEATBALL I’m more familiar with meatball applied to surgery in M*A*S*H, but Chambers has it as US slang for a dull-witted person. Encountered: MET outside A in plain sight plus BALL for dance.
2 What comes in handy in golfing final (5)
DYING The final act for most of us. Hidden in hanDY IN Golfing
3 Witnesses lone rooks flying (7-2)
LOOKERS-ON Notwithstanding “a Crow in a crowd is a Rook, a Rook on its own is a Crow”. An anagram (flying) of LONE ROOKS. The given enumeration confirms the word order.
4 What makes one feel more able, say, to put up rent (3,4)
EGO TRIP EG for say, to put up for OT, RIP from rent.
5 Conflict in unruly bar row involving ecstasy (4,3)
BOER WAR a specific conflict, then, and an anagram (unruly) of BAR ROW and E(cstasy)
6 Show disapproval about tango and current music everyone plays (5)
TUTTI Italian/music for the definition. TUT for show disapproval plus NATO Tango plus I for (electric) current.
7 English spread out around Cape to destroy (9)
ERADICATE E(nglish) plus RADIATE for spread out with C(ape) inserted
8 Some years supporting males in household (6)
MENAGE Some years can be an AGE, here supporting MEN for males.
14 Concerned with a Conservative’s regular turns (9)
REPERTORY RE for concerned with, plus PER for a (tuppence a/per bag) plus TORY for Conservative.
15 Roused to manoeuvres round King’s royal emblem (5,4)
TUDOR ROSE Another simple anagram (manoeuvres) of ROUSED TO plus R for King.
16 What’s part of beach life? Eros, perhaps (8)
ASTEROID A double definition. Starfish are of the order asteroid(ea), though if they’re beached, they’re probably not beach life. Eros is one of the larger asteroids, visited (indeed landed on) by the NEAR Shoemaker space probe in 2001.
18 Old still drink with doctor in charge (7)
ALEMBIC The alchemist’s forerunner of the whisk(e)y still. Drink is the (less potent, usually) ALE, doctor MB, plus I(n) C(harge)
19 Figure month must lead to endless anguish (7)
DECAGON Random moth DEC, plus AGON(Y) for endless anguish
20 Minister’s adviser regularly gets suit (6)
SPADES I’m not sure how far the SP(ecial)AD(visor) has travelled beyond Cummings and No 10, but it makes an appearance here, with gEtS (regularly) added.
22 Dean not including verse in passage (5)
ALLEY For once, dean is not ecclesiastical but geographical, giving VALLEY with the V(erse) not included.
24 Chamber piece too much involving two separate keys (5)
OCTET Too much is OTT, and two more random notes, C and E (again) are separately included.
Simon
Also slowed down by initially entering “Onlookers” instead of “Lookers On”.