Nothing is unwelcome, all is accepted. Have at it.
I am intending this as a reference thread for people tired of scouring the internet for this information. If something new is found, it goes in the list.
Let me just start you off.
The film's NATO trailer showcased a shot of the Klingon commander yelling at camera, later used in the theatrical version's video screen sequence. It's possible this shot was originally filmed in widescreen.
Original special effects for opening, showcasing the actual destruction of the vessels, rather than dissolution
English dialogue for the Vulcan elders during the Kohlinar. Different versions translate the Vulcan dialogue differently, but no subtitled versions match the original English dialogue.
Cut special effects shot of StarFleet HQ.
Kirk defends Deltans when Uhura expresses suprise at Illia's inclusion on the crew list.
An alternate version of McCoy's arrival was shot, showing him carrying a riding crop.
Kirk notifies the crew of the ship preparing for launch via wall communicator.
Early trailers show a shot of the Enterprise's deflector dish igniting, from head on.
The original teaser featured an alternate shot of Kirk saying "Take us out"
A shortened frontal view of the Enterprise was used in TMP, but the complete version appears in a trailer as well as TWOK.
An unidentified shot of Scotty scanning the warp core with some device, possibly part of the activation montage.
The original wormhole effect, a much more crowded and scary looking effect, as appearing in the work print.
The entire wormhole sequence appears without effects and sound editing in the film's NATO trailer.
The original asteroid explosion, different from the stock effect used in the film.
A line was cut from Mr. Spock's arrival from Dr McCoy "Never look a gift Vulcan in the ears, Jim".
The comic version contains a different conversation in the officer's lounge, more dwelling on Spock's decision to become a full Vulcan. This was additional dialogue in the script.
Red alert shots cut out and used in TWOK.
A much longer scene of the first torpedo attack, including Chekov recoiling in pain much longer.
Chapel shares a strange moment with Illia before spraying Chekov down, shown in an early trailer.
A security guard is vaporized by the plasma probe.
Decker and Illia's sex? May have been filmed as it is in the novelization, who knows?
The Memory Wall, which still photographs suggest may have been fully filmed.
A short discussion was cut from the sickbay scene.
Illia's tour of engineering.
A small bit of footage was trimmed from the tear scene.
Kirk cancels the self-destruct order before the spacewalk.
The security guard (Phillips) is mentioned by name in Kirk's final log. You can tell in the final cut that his report has been dubbed in.
There were a few takes of the final shot, including one where Spock made a quite humorous joke, but undermined the tone.
And undoubtedly more to follow.