I voted "OK, but could be better," but there aren't a lot of semi auto .22s I WOULDN'T say that about.
I am an Appleseed shoot boss and have seen a lot of .22s fire a lot of rounds on the line. I have seen several 597s in action, and know a few instructors who use them as their "LTRs." I don't find them to be particularly unreliable, as long as you find the type of ammo they like (this goes for most all .22s). They have a better trigger than a Ruger from the factory, and seem to be capable of a bit better accuracy. I would say the Ruger may tend to be more reliable though... but maybe I just say that because I have owned some that have gone through 1500 rounds between cleanings and still run like champs, as long as they are not fed Federal bulk ammo!
I have heard from other Appleseed instructors that they have had problems with some 597s spitting out the extractors. I have not seen it personally, but it may be a possible issue.
If I were buying a new .22, I would probably go with a Marlin 795. They are extremely inexpensive (around $105 after Marlin's $25 rebate), and I am impressed by what I've seen from them as far as accuracy and reliability go, right out of the box. It just seems like the best deal overall.