I've got my 597 still.
While it is a great feeling rifle capable of surprising accuracy, it is ridiculously prone to frustrating jams.
The clip is your biggest problem, and the only thing you can really do is tap it against something to make sure the rounds sit tight up agains the back of the clip (butts of the rounds against the back of the clip).
The rifle is of poor manufacture and you really ought to get rid of it. I picked up a Romanian Trainer because I'm on a budget and I haven't looked back. The bolt-action also cures my semiauto jamming woes.
Though I've yet to see my friend's 10/22 jam up. That's a quality rifle. Just don't like it that much is all, doesn't feel nice/don't like the look of it.
So yeah, LTS is right. You're really not going to get around this you just have to ditch the rifle. Once in a while you'll get through a clip w/o a jam, but not often, especially after sustended use. Especially with nasty Remington ammo that clogged it up. Learned my lesson there