The unclued lights are of a kind, including one hyphened, all confirmed in Chambers except for 8 across, which is in Collins. Elsewhere, ignore two accents.
 

Across

11    How mud moves like grease, carrying weight (6)
12    Arab American backs musical (6)
17    Recycle rubbish fellow’s left (5)
18    Lawyer with wine for old maid (7)
22    Dismissed god war god beats for boldness (8)
23    Almost cook stews oddly for fish (7)
24    One backing firm strokes (6)
25    Part of neck right back for surgical device (6)
27    Diamond from foreign character, male writer (7)
30    Careful record on film (8)
33    Perhaps it’s lone? (7)
35    Judo move said to give pain (5)
37    Show curiosity between the sheets (7)
38    Officer remains in assistant’s embrace (5)
39    Like some verses from Galicia classified the wrong way (6)
40    Hot dog coming with legal limitations (6, two words)
 

Down

2    Henry: lout and jerk (4)
3    Hide falsity, lacking morals (6, two words)
4    Greeting man loudly providing health advice (7)
5    One really explains map lines (10)
6    Communist catches andirons (7)
8    Shiny fabrics in dresser I cut up (5)
9    Such as radio and TV service by Persian region (9, two words)
10    Like TV’s good qualities (6)
14    Most likely to stick visitor outside of Malta, note (8)
16    Russian royal saw heretics rioting (11)
19    Top courier wandering in the country (10, two words)
20    Drops flier over obstacles (8)
21    Bard’s people turning up crave rain bursts (9)
26    Nervy over time on neither side (7)
28    Promoting unity and love in ethnic conflicts (7)
30    Getting dehydrated, cut whisky in Scot’s bash (6)
31    Old man holding a tin, drunk figure getting smashed (6)
32    Octopus has nothing in soft flesh (5)
36    I’m amazed about current state (4)
 
A first prize of £30 for the first correct solution opened on 10 June. There are two runners-up prizes of £20. (UK solvers can choose to receive the latest edition of the Chambers dictionary instead of cash — ring the word ‘dictionary’.) Entries to: Crossword 2409, The Spectator, 22 Old Queen Street, London SW1H 9HP. Please allow six weeks for prize delivery.