How can I verify that my .mpg files are not corrupted?

Question

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How to check the integrity of a video (avi, mpeg, …) file?

I have a bunch of old home movies burnt to DVD's and CD's. I am in the process of moving them onto a file server, but I am having trouble reading some of the discs. The result is a folder full of .mpg's some of which are corrupted.

• Is there an automated method of verifying that a .mpg file is OK and not corrupted?
• What manual methods are there, which would not require watching through each file in its entirety? (Would just jumping to the last few frames give me a good idea whether the file is corrupt?)