14a Useless hero could be caught (4) - D - E, so it could be IDLE = useless, and it's an anagram of EL CID (hero) without C (caught) Or does anyone have a better idea?
7d Radiation unit? One denying using small number for time taken up (7) Presumably RONTGEN, but the closest I can get on the wordplay is NEGATOR with N instead of T, all reversed, giving RONAGEN. Any...
23a Lady holding title only after her second game (5) C - E - S, so presumably CHESS. I have a theory regarding the wordplay, but I'd be interested to see if others have the same idea.
32d Annulment (6,6) - A - C - L - A - I - N I'm guessing that (6,6) is a misprint for (12) and the answer is CANCELLATION, unless anyone has any better ideas?
22d Right of pair to cross barrier perhaps (6) - R - D - R, if I've got the across clues right (I'm not totally convinced by NOD for 27a Tip some winks?, or HEADGEAR for 29a Mortarboard, especially?)
10d US soldier in time set about battle, seeing venomous attacker (4,7) 40d Runner in wrongful arrest, one safeguarding funds (9) Answers are presumably GILA MONSTER and TREASURER, but GI and MONS...
9d Financial regulator, a comprehensive searcher (11) c - m - t - o - l - r, so presumably COMPTROLLER, comprehensive = COMP, but searcher = TROLLER seems a bit loose. Any thoughts?
3d Dash out of the tube for milk (7) s - u - e - e, so probably SQUEEZE, but can anyone explain the first part of the clue? (I can just about manage to make MILK = SQUEEZE)
34d Install net and be playing game that uses it (5,6) Presumably TABLE TENNIS, but isn't there an L left over? Perhaps they meant to say INSTAL not INSTALL, and some overzealous person corrected it....
52a C20 Italian sports-car company (7) The answer is BUGATTI, so the compiler fell into the same trap that we did at a pub quiz recently. The company was French!
27a No quick way to avoid teacher's pressure (6) - t - e - s Presumably the answer is STRESS, but I can't see the cryptic explanation. MISTRESS minus M1 (not that quick a way last time I...
These are for my mother, not me, so I may not have the wording exactly right. One seems to be TARMAC, but we can't see why: Black stuff Sally found on the bone (6) t-r-a- and the other...
3d Fan eating first of his endless selection boxes? (10) c - o - - h - l - c I'm guessing it's CHOCAHOLIC, and I can see CHOIC(E), but I can't see a cryptic fan. Can anyone else?