The command-line tool mp3val makes quick work of scanning for, and optionally repairing, structural defects in mp3 files. I try to run it over pretty much every file in my collection, on the "can't hurt" principle. It identifies amazing numbers of ostensibly-good files with defects ranging from inconsequential to severe.
mp3val is especially good at recognizing and correcting header deficiencies, such as lack of VBR headers in a VBR file (the source of most wrong-duration and seeking issues). But it will also clear out garbage/corrupted audio frame data, unusable cruft that some players may handle less than elegantly if it's left in the file.
It can even be told to run over an entire directory of mp3's, repairing only those files it finds problems with, keeping backups (or optionally not), preserving timestamps (optionally), and logging the session to a text file (optionally).
And it's free and open source! (The link is to its sourceforge project.)
EDIT: One last thing I forgot to mention. "But mp3val hasn't been updated since 2009!!", I hear you cry. That's very true! It's been working just fine since 2009, and hasn't needed an update. (After all, it's not like the MP3 file format has changed any in the past 2 years!)