I have a 770, which started life as a 710 back in 2004 when I bought it. Got it in .30-06. Along the way my 710 got returned as part of the settlement agreement for a Remington class action lawsuit (think it was related to the trigger) and I got it back with a 770 receiver and stock because they couldn't just change the trigger. Only problem I've had with it was the original magazine came apart in the summer as I was experimenting with ammo at the range. I don't do a lot of deer hunting - I might get out 10 or 12 times a season - so I didn't need anything pricey.
While the action is not the smoothest by any means, it has always shot well. My original 710 liked Federal 150gr Sierra Game King boat tail soft points and would shoot about .75 MOA. The 770 likes basic Federal Powershok 150gr PSPs and will shoot about 1 MOA and several others than shoot close to that. Basically the rifle does everything I need. I doubt it will ever be called to shoot further than a couple hundred yards where I hunt.