I had a problem similar to the OP's. I first started noticing it while using a running app. It would call out splits at the wrong locations and had me at odd paces (2-3 minutes faster or slower than normal). When I looked at the route log afterward, it had me jumping a block over and back at odd intervals rather than tracking down the street.
I started noticing it in the car as well. The icon would be a block away, or start going in the wrong direction or just lose the signal entirely.
I went to the local Apple Store and at that point it wasn't working at all. At the beginning of the appointment it had no signal. It eventually got a signal, but wasn't consistent. The Genius bar told me a they've seen this with several 6's...sometimes it's a bad GPS, sometimes it's 'some bad code somewhere. The chip can't be replaced, so you're stuck being a replacement (at lower cost). So his advice was for me to wipe it and load it as new. He felt confident that would fix everything. Seems like a royal PITA to load everything back on it. (He said not to do a restore)
This was also their solution for why my battery jumps down at 10%-20% ranges and will do the same thing when it charges. I used to be able to run for 2 hours and have 40%+ battery if I streamed music and used my run app. I've had it go dead after 40 minute runs.
I bit the bullet and finally wiped it this morning to see if it'll fix either issue.
Take it to an Apple Store and they will run a diagnostic test on it. If you don't have one nearby, then you can try the 'wipe it and start over' advice they gave me. I'll post back in a few days and let you know if it solved the issue for me.....