Can you export as an IGES, and then reimport as a new part? Obviously this is only feasable if the part does not have any features after it, or they can be recreated quickly. If that is not an issue, you can then run import diagnostics on it when you re-import it, and hopefully fix it that way.
Another way would be to just start using the delete face command on all the bad surfaces. Delete and patch if you can, or delete and fill if you have to (and it works as you want it to).
As Charles mentioned, and I did not see in your question, did you run "import diagnostics" on this file to heal faulty faces and geometry? If you are not sure how to do this, right click on the import feature and select "Import Diagnostics" and a dialogue box wil pop up with these options.