Sigh, apparently tightening the negative lead didn't stop the problem after all.
I got out my multimeter this morning, and did some checks on the battery. No drain, so that's good - the rev counter replacement seems to have fixed that. The battery was reading 12v before starting. When I started the car, before touching anything, the voltage dropped to 11.5v. When I revved the engine, the voltage rose to above 14v and stayed there.
Does that mean my alternator's shot, or could it still be a bad connection, or maybe the battery? (I'm pretty sure the battery could do with replacing). The car seems to be absolutely fine once it's got over the initial startup - revving the engine seems to bring it all properly to life.
Thanks for any help,