The bottom element in my water heater burned up. I took the bottom panel off, and everything inside was scorched - the insulation, the plastic cover, the thermostat - even the edges of the panel. The thermostat still seemed to work, so I just replaced the element - and it runs like a champ now. Can the scorching cause any issues?
Possibly, but without seeing the extent of the damage no one will be able to tell for sure.
Given that you have already replaced the element I'd keep a close eye on the heater for a few days to make sure that there are no problems.
Did you clean everything and check for further damage before you reassembled the heater?