Sorry, this is going to be a long comment again... If some of these things have already been mentioned I apologise.
Yep, I kinda like the Freewheel-intro (is it the same as the solo backing chords?), and got to know about it only recently.
Hmm... Of the rare songs/versions I know, I believe (Father) Mother Son has already been mentioned in this discussion. I've only heard really bad sounding live takes on that though, so if there is an okay version, I'd love to hear it. But are there any other early Priest songs? Mind Conception and Holy is the Man have been mentioned, but played by Priest?
There are two versions of Rocka Rolla. The long version (roughly 4 minutes) includes 3 verses+choruses, two of them before the solo. The more usual edited version (3'06) goes to solo after the first chorus. I have no idea why they cut it (the first verse), I'm more used to the longer one, but haven't found that one on cd yet.
The live bootleg version (1975) of Island of Domination is also interesting, as the verse-riff was noticeably different to the version on Sad Wings.
Likewise, there is a longer jam of the Ripper, which was later cut shorter for the album.
There are two different versions of Diamonds and Rust, which I remember being already mentioned in this discussion.
Blood Red Skies Extended Remix Version lasts a whopping 10'33!! Talk about EPIC!
Some of the simply edited singles from Killing Machine up to Painkiller:
Evening Star on KM/HBfL is 4'06, (some?) singles 2'53. You've Got Another Thing Comin' single is 4'26, on album 5'10. Turbo Lover 4'41, on album 5'33. Locked In 4'01, on album 4'19. Blood Red Skies 4'16, on album 7'51! A Touch of Evil 4'15, on album 5'44. Night Crawler 4'08, on album 5'44.
Also, Beyond the Realms of Death (live tokyo -79, NOT the Cleveland '78-version) has been officially only released on vinyl, not on cd, as far as I know. So if you want to listen to the most complete Unleashed in the East you got to get the vinyl (Japanese one with 4-track EP+Rock Forever (live)-EP (for beyond)+Living After Midnight 12" (for evil fantasies).