Regrading the HR sensor, how firm\tight are you strapping the watch on ? The first few times I ran with the watch (and using MapMyRun) it didn't do a good job. I noticed the tighter it is the more accurate. But I'm not entirely convinced it's not just the watch HR sensor, also maybe MapMyRun wasn't displaying\detecting HR correctly. I could be wrong. I do sweat heavily with the humidity but shouldn't impact the reading if it was developed correctly.
It is the watch bc it is a widely reported problem.