RE: Ruger M77 problem .243
Sounds to me that your mag feed lips are bent/damaged. "Fiddling" with it you are seating the round too far forward and as you try to close the bolt it pushes the round too far forward and out before it can grab ahold of it.
Not to put anyone down here, but the fellows over at RugerForum are pretty good at these kind of questions, a few ruger 'smiths hang out there.
And you have the older M77, "tang safety" looking at your pic. Still nice rifles.. if that turns out to be your problem contact Ruger and they'll help ya out.