I was surprised to see that no one made this before, so here is a module that fixes the broken Android TimePicker.
I consider the TimePicker broken because changing the minute from 59 to 0, or vice versa, increments or decrements the hour, respectively. Since it's common to choose a time by first setting the hour and then the minute, this is really annoying.
This module removes the described behavior from time pickers implemented using the android.widget.TimePicker class.
APK and source for the first version are attached.
The module can also be found on the Xposed repo: net.feichti.timepickerfix
To be clear, I'm talking about the old spinner-style time picker like the right one in this picture, not the pretty one on the left.
I uploaded a new version which adds the fix for date pickers.