First, right click (assuming you're using a PC) the offending song and hit "Get Info", then go to "Options" and make sure the "Stop Time" isn't set to something wonky.
If it isn't, you can try using an MP3 checker. I've used
this (link) to fix songs that are corrupted in that they won't play in iTunes, or that they don't save album artwork. I've never had your problem, but it might fix that as well.
> Download the version that applies to you (assuming PC again, you'd click the first link after the scary red warning)
> Run 'mp3val-frontend.exe'
> Load the offending songs ("add folder/files to validate")
> Check the offending songs ("Actions > scan all")
> And if it says "PROBLEM" on the right column, fix the songs ("Actions > fix all")
It actually rewrites the MP3 file itself, so there are no duplicates and you don't have to mess with the file in iTunes (assuming this works for you), so you should be able to simply play it like normal.