ACROSS
1 Try to spot invisible character in play (5)
GODOT – GO [try] + DOT [spot]
4 Barrier protecting platform for unconventional art (7)
DADAISM – DAM [barrier] “protecting” DAIS [platform]
8 Lip ring ensemble with no strings attached (5,4)
BRASS BAND – BRASS [lip, as in cheek] + BAND [ring]
13 Passage that spans short story about uninhibited people (9)
TRAVERSAL – TAL{e} “about” RAVERS
14 Publish marks off Rhodes scholars etc (13)
POSTGRADUATES – POST [publish] + GRADUATES [marks off]
15 Be rude to seaside town where each dismisses an English dramatist (7)
CHEKHOV – CH{e}EK HOV{e}, each word dismissing an E
16 Sound contented, getting back into bed unclean (7)
CORRUPT – reversed PURR “getting into” COT
17 Rotary engine’s short piece, spun almost completely around (7)
TURBINE – BI{t}, with TURNE{d} “around” it
18 Answer book dispatched virtually having no pages unexpectedly missing (6,7,5)
ABSENT WITHOUT LEAVE – A + B + SENT + WITHOUT LEAVE{s} [answer | book | dispatched | having no pages (virtually)]
21 Rafter on Mississippi hotel attached to back of roof (4)
FINN – INN attached to {roo}F. Mark Twain’s Huckleberry.
23 Settled in house, sister produces fumes from trap? (9)
HALITOSIS – ALIT in HO SIS
25 Observation of lucre paid back but not in full (6)
APERCU – hidden reversed in {l}UCRE PA{id}
26 Not fancy food? It’s arisen unexpectedly (6)
SARNIE – (ARISEN*)
28 Not an original way of multiplying (12)
REPRODUCTION – double def
30 Persecution hurt agreement, with delay of minutes (10)
HARASSMENT – HARM ASSENT, with the M “delayed” until later in the answer
33 I attack old health resort with knife containing boron (10)
SANDBAGGER – SAN + DAGGER “containing B
34 Dead and (outwardly) buried, like parts of a conspiracy? (12)
INTERRELATED – LATE with INTERRED “outwardly”
37 Horseman with lance, not the first person unseating someone (6)
OUSTER – or {j}OUSTER
39 First person expelled from more forward part of China? (6)
SAUCER – I “expelled from” SAUCIER [more forward]
40 With overdose constricting the heart, depressants are marvellously effective (2,7)
DO WONDERS – DOWNERS, with the middle letter “constricted by” OD: DO W{O}N{D}ERS
42 Blunder and nearly get fired (4)
GOOF – or GO OF{f}
43 Be determined to acquire the company? (4,2,4,8)
MAKE IT ONE’S BUSINESS – double def
46 Mozart’s contemporary position in exotic dress (7)
SALIERI – LIE in SARI – which may or may not be exotic depending on where you come from…
47 Cheese from Monterey urgently recalled (7)
GRUYERE – hidden reversed in {mont}EREY URG{ently}
48 Title composed by Beatles’ leading pair? (3,2,2)
LET IT BE – (TITLE*) by BE{atles}, &lit
50 Too easily hurt at the workplace, introducing metric works, the fourth brought in later (13)
OVERSENSITIVE – ON SITE, “introducing” VERSE and then later IV [the fourth]
51 Way to cure turkey that won’t burst into flames (despite appearances) (5,4)
SMOKE BOMB – SMOKE [way to cure] + BOMB [turkey]
52 Get off course to westernise, apparently (9)
DISORIENT – or a punny reinterpretation of “dis-orient” to mean something like “occidentalise”
53 Greenhouse gas meant he worried (7)
METHANE – (MEANT HE*)
54 Rough outskirts of Derby found on visit (5)
SEEDY – D{erb}Y found on SEE [visit]
DOWN
1 Horrendous rates charge one received without being asked (4-7)
GATE-CRASHER – (RATES CHARGE*)
2 Duke, libertine and noted sailor (5)
DRAKE – D + RAKE
3 Difficulty in setting up extremely great Russian funds after support diluted? (8,8)
TEETHING TROUBLES – G{rea}T + ROUBLES after TEE THIN
4 Refuse to acknowledge capsize without vessel identification (7)
DISAVOW – reverse all of W/O VAS ID [without | (medical) vessel | identification]
5 Rebuff hardened tart, keeping the French lingerie etc? (9)
DELICATES – reverse all of SET ACID [hardened | tart] “keeping” LE
6 Pretender’s scion imprisoned by Roman emperor (12)
IMPERSONATOR – SON imprisoned by IMPERATOR
7 Pests I shut in religious buildings (10)
MOSQUITOES – I + TO [shut] in MOSQUES
8 Inlet of considerable width and great height (5)
BIGHT – or BIG HT
9 Flexible fitting installed in a low bar (8)
ADAPTIVE – APT [fitting] “installed” in A DIVE
10 Parisian who stops married woman returning to worm (6)
SQUIRM – QUI [Parisian “who”] “stops” reversed MRS
11 Aristocrat losing head’s spoken of natural wastage (9)
ATTRITION – homophone of beheaded {p}ATRICIAN
12 Perception of part of field: is CERN mentioned? (11)
DISCERNMENT – hidden in {fiel}D IS CERN MENT{ioned}
19 Replace a plant’s dried up basin (7)
SALTPAN – (A PLANT’S*)
20 Somewhere to go from ’ere includes one place inside another (7)
ENCLAVE – LAV [somewhere to go], “included” by ‘ENCE [from ‘ere]
22 Heading away from States I had blue and white flowers, keen to raise saving target (6,2,8)
DAMSEL IN DISTRESS – reverse all of {a}SSERTS + I’D + NILES [blue and white rivers] + MAD
24 It’s covered in Ypres mud, getting a dirty mark (6)
SMUDGE – hidden in {ypre}S MUD GE{tting}
27 Plant’s energy lost in time disturbance (6)
YARROW – Y{e}AR + ROW
29 Herts town, neither small nor very relevant to youth (7)
TEENAGE – {s}TE{v}ENAGE
31 Record possibly first released by later engineers (7)
EXTREME – {n}EXT + R.E.M.E.
32 Breaking into 31, fellows start on theft (12)
INFRINGEMENT – IN FRINGE MEN T{heft}
33 Doctor half-heartedly neatens up, accepting hooligan’s punishment is self-serving choice? (11)
SMORGASBORD – reversed DR GRO{o}MS, “accepting” ASBO [that’s an AntiSocial Behaviour Order, American chums]
35 Tailor badly misses stripping (11)
DISASSEMBLY – (BADLY MISSES*)
36 Ethical travel company heading for old city is filling space (10)
ECOTOURISM – CO TO UR IS [company | heading for | old city | is], “filling” EM
38 Son breaks down, has repressed feelings (9)
SMOULDERS – or S MOULDERS
40 Remedy sipped, say, for this? (9)
DYSPEPSIA – (SIPPED SAY*), semi-&lit
41 Bravery of Scotsman caught in glen (8)
VALIANCE – IAN C in VALE
44 In triumph, presumably, nothing is free (7)
UNLOOSE – if you UN-LOSE then presumably you win! Insert O into that. Full marks to the setter for audacity.
45 Landlord with gold taken away? (6)
LESSOR – or LESS OR
47 Flash grand, something that collects in pocket (5)
GLINT – G + LINT
49 Expression in French, too European? (5)
TROPE – TROP [in French, “too”] + E
Liked the Roman emperor that wasn’t Nero at 6d and the convoluted wordplay for such as ECOTOURISM, OVERSENSITIVE and the incredible reverse on DAMSEL…
Well done on working out 22d – I got it from the crossers and the definition but I couldn’t even begin to parse it.