34a - military jargon for 'intelligence', with the 3 core letters of 'battle' going around 'no good' [one letter being a misprint].
39a - military jargon for 'intelligence' 'long piece' (of material) around 'i' for 'current' [one letter being a misprint].
23d - add a letter to the 2nd word - 'offend' (obscure) 3 letters [think of the usual prefix for 'sleep'] + 4 letters for 'nobody'.
24d - Answer is a republic (with a misprint) the obscure word I mentioned earlier is something akin to slander.
31d - The first 'regular' is a soldier (US), the second is a 3 letter synonym [reversed] def 'holiday homes'.