16/17 (four words in total) is a work by 11 which suggests the remaining unclued lights. Five clues contain a redundant word; these can be rearranged to provide the twenty-two unchecked and cross-checking letters in all unclued entries.
 

Across

 
1    Take lead from better Iraqi writer (6)
5    Opposed awfully stupid ado with journo (8)
10    Headgear as Scottish chill’s endless (4)
12    Religious leader lost heart in harvest (4)
14    Secretary, one keeping distance, is a dish (6)
20    Hindu custom, say, cut short during earthquake (9)
21    Some work as soil almost covers house (7, hyphened)
23    Girl touring meadow runs back wanting foliage (8)
24    Tennis champ’s girl is a scorcher! (5)
28    Eleven animals around duck (8)
32    Notice prison walls tend, initially, to get harder to climb (7)
34    They alter dimensions in French recipe for filling drinks (9)
38    Advancing rubles, record income (5)
39    Aeneas noticed reckless speed around Italy (6)
40    Bristle, rigid one (4)
42    Case in truck that’s reversing (4)
43    Clumsily daub lobby, revolting Jordanian royal (8)
44    Dunciad deliberately holds return of old ballads (6)
 

Down

 
1    Sceptical account about rebel military intelligence (8)
2    Oatmeal’s OK with an exotic fruit (12)
3    Imprint name with chisel around (6, two words)
4    Socialite, heartless blonde, gets stood up and declined (5)
5    Ineffective people, dandies losing their fourth épée (4)
6    Imagines raging sea tide (7)
7    Farmyard animals under pressure — they must perform (7)
8    Left priestess burning up cooking ingredient (6, two words)
9    Oh no! Germany and Spain almost ready for war (6, two words)
13    Spreading lies, ‘Sun’ is tasteless (7)
15    Mince pie the French teen rebel made holes in (8)
19    In southern India, woman’s pale Asian coat (8)
22    Soaring verse in which we discover leader of squadron flies (7)
25    City area with ends serviced with connections (8)
27    Weight of carp with two tails? (7)
29    President to veto a Japanese art (7)
30    Forbidden drink judge’s imbibed (6)
37    Roguish artist sent up church (4)
 
A first prize of £30 for the first correct solution opened on 7 October. There are two runners-up prizes of £20 (or, for UK solvers, the latest edition of The Chambers Dictionary — ring the word ‘Dictionary’). Entries to: Crossword 2131, The Spectator, 22 Old Queen Street, London SW1H 9HP. Please allow six weeks for prize delivery.