Is it OK to install a TV mount when it can't be attached to a stud at all mount points?
If you are concerned about the weight an easy solution is to put a sheet of plywood (or nicer wood, if it will still be visible once the TV is in place) across 3 studs.  Secure it with 2 screws into each stud.  Then screw the wall mount into the wood.

Doing it this way will definitely support the weight of any TV you might try to mount.  And allows you to mount the TV exactly where you want it without worrying about where the studs are.

You can paint over the wood to make it blend in with the wall but in most cases it ends up nicely hidden by the TV anyways.