The filing system itself should not make any difference to any bad sectors but i am wondering if you have had some bad sectors reallocated by the drives firmware due to writing to the sector while formatting to ext4 or some such.
Does anybody know if this could simply be due to the ext4 file system? I'm trying to figure out why Windows would have this problem while Linux doesn't.
I would perform a SMART test on the drive and see what that returns. Most newish drives are SMART capable.
From the terminal
sudo apt-get install smartmontools
This assumes your drive is sda.
sudo smartctl -t long /dev/sda
It will take a while to finish. When it has finished
Post the results back here.
sudo smartctl -a /dev/sda