I bought a 710 - the predecessor to the 770 - about 5 years ago and it's been a good rifle. Good accuracy. Bolt is not as smooth as more expensive rifles, but it's never been a problem. I believe the barrel is actually press-fitted into the receiver and not pinned, but either way it really doesn't matter. The only reason anybody has ever provided for not liking that feature is that "you can't change the barrel". Who buys an entry-level rifle knowing they would shoot it that much anyway?
Also, the 770 does NOT have a plastic sleeve that the bolt rides on. My 710 does have one and it's just one less thing to rust as far as I'm concerned. The plastic sleeve was discontinued during the last couple of years of the 710 production. I did look over a 770 in a shop a year or so ago and the bolt was much improved over my 710, but not as slick as my 1903 Springfield made in 1931 (which is my only other bolt rifle other than a .22).
The only safety recall was for
some 710s that were made from
July to October 2002. That is the only recall on the 710/770 and was only related to a safety spring.
For all the admonitions to buy a used rifle, remember you may be buying someone else's problem unless you know what you're looking for. That's one of the reasons I bought my 710. I didn't want to spend $500+ on a rifle I wouldn't use all that much and I didn't know what to look for in a used rifle. The 710 was my first rifle and I went with Remington because of the name and because I liked the rounded stock of the 710 over the squared-off version of the Savage 110/111 at the time.
My 710 hasn't left me "wanting more" nor will anybody here be able to tell you the difference between a real hunting applications and "non-real" one that the 710 wouldn't be able to handle.
I've encountered nothing in actually
using my 710 that would make me not consider buying a 770 if I needed another budget rifle. I might get something else, but then again I might just get another Remington.