I have a field gauge I will take with me if I am thinking of adding another mosin. Most rifles I can get to still have cosmoline throughout, so I'll see if I can wipe off the bolt and clean the chamber enough to check for proper spacing. I haven't seen one out of spec, but for about $35 better safe than blowing up in your face at the range. You can also check the crown, if it is damaged then you know the rifle will not be accurate. If it is counterbored then it may be fixed or not. Checking the barrel for pitting is a lot less precise if it is filled with cosmo so that is always a question, but for the money it is not too big of a deal as long as it is safe to fire and has a good crown. I also look at serial numbers, I like matching numbers and not frankenrifles. Mostly personal preference there as I like these for their historic value and having one that came from the arsenal as one unit means more to me than one someone cobbled together later. Next you also need to look at hex or round receiver, if round then high wall or regular, manufacture date, and arsenal stamp. All of this would be personal preference and I would suggest looking over the link from Jvance325 as that site has tons of good info on all this. If you're just looking for a shooter then most of that won't matter to you.
If you do pick one up, then welcome to the club and good luck on surviving the mosin bug. These rifles are a ton of fun to shoot, and where else are you going to be able to find a high power round for under 20 cents each! Very cheap to shoot, especially if you are not used to shooting a rifle. You'll know what I'm talking about the first time you take it out to shoot