Eureka! I have located the problem I've been having.The culprit is not Squid nor is it NFS. In a sudden bright moment I realised it was mod_deflate which is gzipping the mp3-file! Some time ago I implemented a new configuration for it, which seems to be causing this cut-off. With mod_deflate disabled, the Content-Length header reappeared and the Redbot.org error "A ranged request returned the full rather than partial content" disappeared.
Thanks for your help Amos and Henrik. Regards, Fili