https://thegreatmodel8.net/

I just disassembled the barrel assembly on the .32 Rem model 8 and found that the locking shoulder block on the barrel has a slight wiggle to it. Is this a major problem or is this pretty common? The wiggle isn't major but you can feel it and see it.

target, I'm not sure what the "locking shoulder block" is, if you can snap a photo of it I'm sure we can get your question answered

The barrel extension for the locking lugs. The piece threaded onto the barrel that the bolt locks into.

I'll have to get a picture later.

The barrel extension should never be loose!

Any good way to tighten it up?

I've never personally come across one that is loose. On many of the rifles I've actually looked into, Remington put a witness mark on the underside which I'm assuming was for headspacing. If that's present I'd pay careful attention to getting it back right.

I'll see what I can manage. I am sure I can figure something out on it. Looks like they used the rifle for years like this too. Once I figure something out that shows results I'll post my findings.