My starter button is acting moody 

Sometimes 'yes, I'm ready' and sometimes 'no, not this time' (just quiet), so I'm thinking bad contact...
Hasn't been opened for six years - sometimes wet, but doesn't live outside.

Anything else? Parts that usually fall out? Known difficulties?

I don't recall anything that's a surprise, parts jumping to freedom, etc.

Take pictures of how the wires go before removing screws, and keep the screw locations the same at re-assembly.

Speeddog has it right. No surprises waiting in there. The left one is a tad fiddly, as there's a fair bit of stuff in there, but the right one is a doddle.

Just don't let the smoke escape and you'll be 

Opened it - couldn't get it off to investigate the connections because my throttle wire is on top of it (180 degrees), but it was clean and dry as far as I could see. I gave it a generous spray of 'connector protector grease spray' and now the problem is gone or at least hiding itself. Maybe it was just mechanically dry....