1st thing is to strip and clean the gun as per instructions.
Next thing would be to go to
www.rimfirecentral.com and get in the remington section and start reading about the 597's. I did that and will try to condense what i learned.
Lots of them shoot fine out of box but some have differing problems that are easy to solve!
1. Failure to eject. Remedy buy this 'edge extractor' from Volquartsen
https://www.volquartsen.com/vc//pages/public/ListItems.jsp?id=16 scroll down to see it...and while your at it...also purchase the target hammer to reduce the trigger pull.
2. Failure to fire. Cause of this is usually because the bolt didn't slam back far enough to reset the trigger. Remedy is to shave the little rubber bumper down a tad...its easy to do when you have the gun apart, just pop it out and take it to a cutting board and cut a sliver or two off it with a sharp knife and re-install.
3. When you put the gun back together when its clean...only tighten the two tiny screws that go in behind the rods...until they touch. In otherwords...do not 'tighten' them....light snug is all they need. If they are too tight, and they can be right from the factory....also causing you your current problems btw...they bow the rods and the bolt doesn't slide back and forth as freely as it should. That should cover it. This may actually be the most important first thing you try! Take gun apart and clean it...then make sure when you put back together...these screws must barely be snug.
I have the .17 hmr and out of the box it would occasionally not reset the trigger on the 17 grain v-max ammo(no trouble with the 20 grain xtp ammo) and it occasionally didn't want to eject one. So i followed all the instructions off the rimfire central website, i shaved the bumper, very lightly 'snug' the rod screws, installed the edge extractor and target hammer and now the thing is a few hundred rounds without any problems and has a nice trigger. I also put a trigger shoe on it and it reduces felt pull a little more.
And one last tip...if you have the magnum it might have two springs on each rod...if so...the gun is a pain in arse to reassemble with all the springs...i just reassembled with the larger diameter springs and it works just fine and is a treat to take apart and clean and reassemble etc. Much easier...that last tip i also got from rimfire central.
Mine is very accurate too btw, it was out of the box....now its just super reliable too.
The only time my gun will give me trouble is if i have a round in the chamber(bolt is closed) and i put a magazine in...it can change the angle of the next round in the magazine(sort of flattens the angle out) and not insert the next round after the first shot. I find that you install a magazine with the bolt open, then you close the bolt inserting the first round into the chamber and leave it alone(don't pull the magazine out etc....then its 8 shots as fast as you can pull the trigger...everytime). Thats the only thing i can think of that will give you trouble if you do these things.
Its worth it too...i'm super happy with this gun and i'm not much of a tinkerer...and i found this easy to set up right.
B