With an oscilloscope you could also see the 'noise' and what is left of that, after the input capacitors (and whatever else there is) on the amplifier board..
Relatively cheap and reliable ones are being talked about on eevblog forums - expect about US$ 300 for a decent 4 channel osci with a bandwidth of 100MHz. I got myself for home use a Rigol DS5054 (4ch, some logic analyzer capability) and a Owon SDS7102 with battery (2ch, floating mains measurements) - software wise the Rigol is more mature than the Owon.
Nowadays should be possible to get a 4 channel battery one for maybe US$ 500 with 100MHz.
But yeah, check out aforementioned forums, they discuss this stuff all the time and also do hacks of the gear to improve it - of some of the regulars approve of something and it's been out for a while (to find bugs/problems), it's pretty safe bet and you'd have a large community to help with problems.
Yeah, some are like that. Make sure the mains cable going into that box has a pull-inhibitor attached to the cable, so it can't come out and you get to touch the bare powered wires.
And it might be a good idea to invest in some residual current miniature circuit breakers, if you build stuff like this more often (mostly only installed for wet-room sockets, they're not much more expensive than simple MCBs, but will save your life if stuff goes wrong).
As for the wiggling - try to get some from a brand manufacturer or change the clamping system.
One I like is called cage-clamp. No idea if available for board mount and 230Vac though..
Depends on the type of washer, metal ones usually between screw and board, with rubber, I'd tend between standoff and board.
Avoid conductive TP (better heat transfer for CPU/GPU applications), use ceramic based types for electronics (usually white) and be aware that some can release the fluid over time (if you get them from ebay), which then goes wherever it wants.