V1 tags are stored at the end of a file, V2 tags at the beginning.
Does M3diags show one V2 tag plus an offset where the audio data starts? Or just the V1 tag? (what does mp3tag say?)
What you hear is the tag data as apparently the player does not identify that part of the file as metadata - as the player probably can only cope with v1 tags.
If on the other hand mp3diags only reports a v1 tag in file that clicks then the start of the file is really damaged.
And further: if - after you have tagged the file with mp3tag - neither mp3diags not mp3val report corruption then it is not very likely that mp3tag is the culprit.
What I would try also: check a file that you have not yet tagged with mp3tag with both programs and see what they say. Hopefully, all files are ok. But if not ... it would mean that the errors crept in somewhere along your workflow.
Edit: I would like to add a link to this thread where some other poster complained about noise at the beginning of a file - perhaps you recognize something:
[X] Mp3tag corrupts every mp3 file after editing the tag .