Is there nothing built into MusicBee to check a files integrity? I know Foobar has something in preferences, but I think it can only do VBR MP3s.
There's nothing built in to MusicBee for this. You're right about Foobar - it's called "Rebuild file header" or something similar and that's what mp3val does too. It's a problem with VBR files that have incorrect information in their file header. Audio programs use sample rate and file size etc. to determine the duration of a track. If that information is wrong the calculated duration is wrong too. For the files you mentioned you may also see MusicBee report the bitrate as something stupid like 32kbps.
I have thousands of songs, It would probably take forever to do them all.
mp3val is command line but includes a GUI with drag-n-drop support. You could just drop your music folder on it and it will check - and optionally fix - thousands of a song in a matter of minutes.
Yes I checked the bitrate of the song and it said 32kbps when it should be 256.
I ran the entire album through mp3val as Pingaware suggested.
Here is what it says for the first incorrect track.
Analyzing file "C:\Desktop\1983 - Earth A.D. & Wolfsblood\01 Earth A.D..mp3"...
WARNING: "C:\Desktop\1983 - Earth A.D. & Wolfsblood\01 Earth A.D..mp3" (offset 0x3c196c): Garbage at the end of the file
WARNING: "C:\Desktop\1983 - Earth A.D. & Wolfsblood\01 Earth A.D..mp3": VBR detected, but no VBR header is present. Seeking may not work properly.
INFO: "C:\Desktop\1983 - Earth A.D. & Wolfsblood\01 Earth A.D..mp3": 4945 MPEG frames (MPEG 1 Layer III), +ID3v1+ID3v2, no VBR header, CRC
Done!