Neatness as such isn't a requirement in the regs as far as I know and insisting on tidying a DB up at the customers expense is overstepping the mark if he was just inspecting and testing for a certificate of compliance. If there were safety issues such as incorrectly sized wiring, incorrectly terminated wiring, incorrect wiring colours etc then he shouldn't have called it 'messy', he should have explained it was not compliant but was easily repairable on the spot.

If the tripping fault was caused by wiring he's done in the DB then you shouldn't get a bill for the repairs. There's always a chance it's caused by something unrelated in which case he'd be within his rights to bill you for the visit. Problem is if a contractor is underhanded he could twist the blame to make things in his favour and it's very difficult to prove otherwise. I'm guessing you already have trust issues with the contractor so maybe you should call another contractor in for the tripping fault and just foot the bill anyway. It's kinda a rock and a hard place situation.