It's a known bug with the current KitKat build that has been in place since the update. The good news is that there is supposed to be an update that will fix this issue. A Moto employee on G+ said that the update would be sent for carrier testing to Verizon at the end of June and that testing usually takes 3 to 5 weeks - so it should be here, finally, soon.
There is definitely at least one thread about this here but I'm not going to find it for you right now. However, see this thread:
https://forums.motorola.com/posts/ef7321672a
As for the two-step problem, you should be able to create an application-specific passphrase that will allow you to log in to your Google account without the second factor. Once the update is delivered you can rescind the passphrase, as the problem should not be recurring.