We had a 788 in .223 as our station rifle for about 30 years; it finally became too expensive to repair/maintain, but by then it had fired many, MANY thousands of rounds, and had a hard life.
About the only mod we did to it was replace the trigger with a Timney about 15 years back.
Yep; magazine is loose as buggery. It seems to be a 'feature' of the 788. I understand the latter mags were plastic, but ours are metal.
Here's a link to figure out when yours was made:
https://www.remingtonsociety.org/manufacture-dates/[Rummage around a bit on this site to get a more firm idea of yours..]
Overall, the 788 was a great little budget rifle.
However, a few problems kept coming up:
1). Dependant on the brand of primer in the ammo we were using, the firing pin would pierce the primer, and then the small disc of metal would blow back into the bolt itself. Once a few of these had happened, the firing pin would seize up, and the bolt has to be disassembled to clean all the discs out. Initially, we trialled adjusting the firing pin strike length (distance it protrudes out of the bolt face), but you walk a fine line between repeated misfires, or holes in primers. Upon advice, we switched to a heavier primer in our reloads, and while we solved most of this, we were still getting firing pin jams every so often. The firing pin has a 1-inch long tip which is just sitting on the end of the pin proper, and it's easy for this tip to get bent.
[If we'd sent the bolt to a decent gunsmith, I'm sure they could have resolved this by machining a larger firing pin hole, and pin to suit, but decent gunsmiths that you can meet face to face are a bit rare in outback QLD, and this rifle wasnt worth a lot...]
2). The 788 had a reputation for the safety being inherently dangerous due to it's design. Something about the safety getting dangerous over time with use. Advice on a LOT of the forums is to never trust the safety AT ALL. I couldnt figure out why we'd not had any problems with ours, but then I found a post by the gent who said that all of the problems with the 788 were easily fixed, and he said that the safety issue was resolved if you fitted a Timney trigger. I then realised that we'd fitted a Timney about 20 years ago, to improve the trigger, so now understood why we'd never encountered this issue.
3). The 788 had a reputation of being extremely accurate, and the .222 was supposed to be the most accurate of them all. From what I have read, they were one of the first (budget) production rifles that pretty much shot sub-moa out of the box. If the barrel is half-decent, you should find it is a keeper.
4). Our extractor failed ~18 years back, and it was cheaper/simpler to have a gunsmith machine a sako-style extractor setup into the bolt. I see the old 788 ring-type extractors are occasionally available through people like rebel Gun Works, so you mightnt need to do this.
5). SOMEWHERE in this rabbit-warren I call home, I have a bag of the bits & pieces I pulled off our 788 before it was chopped. All the screw-on metal bits, and a couple of stocks. I cant recall if I removed the trigger or not(I hope I did), but I did find the Timney packet with the original trigger in it, if thats any help. Pretty sure there is a couple of spare magazines, if you'd like them. HOWEVER, dont hold your breath while I go look for them!
6). We trialled a 'Champion' brand of synthetic stock on our 788 for a few months, but it broke in half! Never had that happen on either of the wood stocks we have here for it...
Cheers,
Rod.