Did you check to make sure all the components are tight including the bushings and the main flipper plate? I assume that's what you mean when you say loose side to side? Or do you mean the flipper bat is actually loose on its post? If that's the case, you need new flipper bats.

Could be a broken bushing...that happens a lot.

You really should replace the bushing whenever doing a flipper rebuild (I know they're not in the kits, but they should be). Red loctite was probably used on the previous rebuilds hence why the screws broke.

Yup. Always use blue loctite.

You probably broke off the screws because there was a nut on the underside

Don't know about those guys, but this guy has been reassembling pins for 30 years, I've never applied a drop of the stuff. And nothing has fallen off yet.

True that.

I've used blue on a few things that take excessive vibration or trouble areas but I agree, it is generally not needed but certainly doesn't hurt.

I've never needed it on a pinball machine either.