Users are reporting problems about installation of the update. The update is stuck downloading on the device and crashes during installation. Users coming from different versions of iOS 7 is reportedly experiencing the problem so we can say that this problem is not just isolated from one version.
Quick fix is to hard reset your iPhone or iPad by holding sleep and home button for up to 15 seconds or until the apple logo appears.
Users are also reporting issues with not being able to use their exchange accounts. The battery problem seems to have not been fixed yet too. Rear camera not working and only displaying a blank screen might also be encountered. I've seen also a report about contact information gone missing, I too is experiencing the same issue (this explains why some of my contacts can't be seen on the contacts app but when you access the info from iMessage contact info you can see it). Contact syncing issues and a lot more.
If you I want to see more problems affecting users who updated to 7.1.2 , you can see it on discussion.apple.com , just search for 7.1.2 .