JKDefrag uses the Windows API to move files, so the program itself is completely safe. The API does a lot of things to prevent any corruption, but since a crash is not normal, everything is possible. You should definitely run checkdisk on your partitions. This does not check file integrity though.
My disk has a lot of important files that cannot be corrupted, so I'm just paranoid that now there is a corrupted file(s) somewhere on my disk.
Every file that is not backed up is not an important file!