Anybody with a 783, you might want to check the the action retention screws. I know a guy that had one fall out, and went unnoticed for a while. He searched local gun shops and online for replacement screw, and while some online shops listed the part ($5.00), none stocked it. Finally ended up calling Remington and they sent him a new part FOC. Remington has, in recent years, taken flak for QC (which they seem to be correcting), I have always found their customer service to be pretty good.
I guess on a rifle that sells for under $300 this type of thing is not a shocker. The rifles seem to shoot well.