I thought I'd let you guys now...
When I was browsing through the Album list I noticed that one of my albums was gone. I later found it under "?" and tried to figure out why it appeared there. I added the files to the playlist and discovered that Foobar didn't read the ID3 tags, neither v1 or v2.
Decided to try the files in Winamp and Mp3tag v2.35, and both apps could read the ID3 tags. Selected all tracks in Mp3tag and pressed save (didn't make any changes).
Now all files workes in Foobar also. Would be interesting to know what the problem was and if I have more files like this.

Sorry, but I can't tell you what the problem was because your files are already magically fixed by Mp3tag

foobar2000's ID3v2 tag implementation adheres strictly to the standard where Mp3tag includes some workarounds for buggy software. Maybe there was some ID3v2 frame within your tag, which was written by a buggy writer.