The compass has always seemed a bit off to me. I'm not sure how to get a quantifiable answer to this question, but the GPS tool I used to troubleshoot does have a compass calibration tool. I ran it last night and it appeared (again just to look at it) to be more stable on my drive in to work today.
I tightened the screws using a small screwdriver, and I don't think given the scale that I could have overtightened them; the screwdriver I was using was pretty flimsy. The results after a full day of use are astounding. While I didn't look at the GPS tool this morning, yesterdays driving showed error feet which occasionally dipped into single digits, something I've *NEVER* seen before. It appears to have completely solved my issues. I'm stoked that I don't have to troubleshoot this further, because my next step would have been to Odin back to stock to ensure that it wasn't ROM related. At this point, at least in my case, that's been ruled out.
As a side note, I will admit that my phone has been dropped a few times; nothing crazy, no pavement, always in S-View case, but who knows, maybe enough force to cause some loosening.
VZW Samsung Galaxy Note 3 [NC2/SafeStrap/BajaROM KK build 16]
Gear 2 Neo presently bone stock. Tizen SDK/Eclipse, intend to play soon
Asus Nexus 7 (x2, kids) Running stock, ulocked & rooted
Google ChromeCast and MediaCenterCast
PLEX Media server as a companion to ChromeCast. Love Plex.
Dual boot Droidx86/Windows 8 Preview Now running Win8.1
Motorola Droid X2 on VZW Running CM10a3 by DKZ