A few seconds of footage were cut from the simulator scene.
An interesting note, the IDW comic version of TWOK has exterior shots showing the Enterprise's destruction during the Kobayashi Maru, contrary to every released version of the film.
A brief snippet of deleted footage from the present scene including the statement of Saavik being half-Romulan. Additionally, Spock asks if Kirk is feeling oppressed by something.
A longer take of the McCoy/glasses scene.
Chekov originally had a different log entry, designating he was duty officer.
Carol and David originally had a longer scene with each other.
Chekov spotting a child in the Botany Bay window, and an infamous scene showing a stuntman in blackface standing in for Terrell.
Terrell finding Khan's baby in the Botany Bay.
Marla McGivers (or Noonien Singh?)is mentioned by name in Khan's speech.
The Ceti Eel scene was originally a little longer and more graphic.
Kyle and Beach attempt a rescue, but Terrel (under the eel's power) convinces them to beam aboard Khan's crew.
Like the first film, Spock and Saavik originally spoke English in their conversation.
A scene detailing Sulu's promotion. (BTW Sulu was originally intended to have control of the Excelsior in THIS film.)
An alternate take of the scene of the scientists arguing.
Carol's narration during the Genesis tape scene was changed to give a different explanation of the Genesis effect (actually it was to provide implication that Spock could return).
An alternate take of the discussion in Kirk's quarters.
Kirk had a line about Chekov during the first Reliant encounter.
Scotty is seen telling the other engineers to stay at their posts.
The original cut of the Enterprise's attack had Khan moving across the bridge shouting at Kirk.
At one point Kirk recalls the "blind as a Tiberian bat" line while orbiting Regula 1.
McCoy reveals he had worked with Terrell.
The scene of David attacking Kirk was reshot at the studio's consent, and all subsequent scenes in the cave as well. The original version featured David leaping out of a cargo container, as shown in the IDW comic adaptation.*
A scene showing McCoy working on Chekov's ear, and denying David passage to the bridge.
Chekov later wakes up and is taken to the bridge, David soon follows.
A scene of Khan's baby in the transporter room next to the detonating Genesis device.*
Khan's final reaction shot before the Reliant' destruction.
The original funeral scene was slightly longer.
The scene between David and Kirk had different dialogue initially, redubbed at the studio's consent. "I should be on the bridge" "Are you running away from me?" "I suppose I was."
There was brief scene cut out between Saavik and David on the bridge, paving the way for a later romance.
The original ending lacked Spock's tube on the Genesis planet, making it seem as if he really was
dead. Meyer reshot it after studio pressure and a bad test screening.
(note)Although the new ending was intended to leave an opening for a sequel showing Spock's returning, many materials at the time seemed to show the public thought he was really dead, in particular the original DC comic book series.
*Might not be right on this one, someone help me out!