For me, the accepted answer didn't work for some reason. Maybe UnrarX has changed something in their later versions, or there was something funny about my files. It just didn't show the correct result for my files. Anyways, here's how I solved it:
I downloaded the rar command line tools from Rarlab. Download the 'RAR for OS X' package. Even though it says trial, the unrar part is actually freeware. To test the archives run
unrar t /path/to/file.part01.rar
It will show you exactly which files are corrupted. After replacing the files, you can extract using a gui program or by running
unrar x /path/to/file.part01.rar