Unless you are looking at some old milsurp bolt action rifles then there isn't much else to check. If you are looking at milsurp that opens a different set of things to check.
Agree with Jimro. Other than chekcing the Bore and Crown, I cycle the bolt to see how it operates and I also like to be able to pull the trigger. I shoulder the rifle and check the length of pull and how comfortable it is to shoulder and rest my cheek on the stock to see how comfortable the cheek weld is. Other than that, there is not much to it aside from asthetics that appeal to you individually.
I like to take the stock off if I can to see if anybody has done any work at glass bedding or free floating (themselves.) I generally guess that only people that shoot a fair amount will try those types of things and if there have been attempts at "accurizing" the rifle has probably been shot more than I like, and may have accuracy issues.
