How do I know if/when tuckpointing is necessary, especially if I finish the basement?
How do I know if/when tuckpointing is necessary


You need to tuckpoint when the existing mortar is failing. That could be that it's water damaged, cracked, or just getting weak. To see if it's weak, take your key and drag it along a joint...if it's easily flaking off and scratched...or worse, crumbling, then it's time to chisel out the damaged mortar and tuckpoint. 


  especially if I finish the basement?


Well, that's the catch. You can't tell if you need to tuckpoint your joints unless you can see the joints. So you can't exactly just finish the exterior wall and assume you're good to go. New joints should last a long time, but they will eventually fail due to the inevitable moisture movement that happens in a fieldstone wall. 

As such, you probably don't want to finish the exterior walls. I'd argue you shouldn't finish a fieldstone basement at all, but I've seen it done where they build a floating wall 2' or so inside the exterior wall. This gives you a walkway around the perimeter to keep an eye on things.