Kevin's Watch

Quest for Iscandar
In the original Japanese version, there was a lot of "damn" and "damn you" that were translated out of the English version. Most likely the dubbing crew realized that the target audience in America consisted of kids, so they didn't want this sort of language in the series.
There was a scene during the Yamato's first warp where Yuki's (Nova's) clothing warps in and out - again, not a scene suitable for young children, however standard fare for Japanese animation.
A scene which was pulled from the American version was the history of the original Japanese Battleship Yamato. The battleship was shown being sunk by American pilots, along with the captain lashing himself to the bridge as it went down while the US pilots saluted. The translators took into account the amount of people who fought and/or died at Pearl Harbor, so the scene was removed.
When Yuki, Kodai, and Analyzer (IQ-9) land on Titan, they are captured by a Gamilon tank commander. We are led to believe that the tanks were robot controlled, but the death screams of the Gamilon drivers were masked out of the dialog. Kodai grabs a gun from the ice and shoots the Gamilon, however the American series shows an avalanche and Nova exclaims that the Gamilon was buried. Many other such deaths are masked out, since at that time blood in American cartoons was unheard of. (At least they didn't pull the cheesy GI Joe method of giving every downed pilot a parachute.)
A rather dramatic scene towards the end of the original series was after the Yamato destroyed the Gamilon forces on their own planet. The crew of the Yamato is surveying the damage and casualties, while Yuki and Kodai are on the deck of the ship. In the American translation, this entire scene is cut to Nova crying about the amount of fighting, and Wildstar comforting her by saying the fighting is finally over. In the original series, this scene is much longer, and involves the two of them realizing that in keeping the Gamilons from destroying Earth, they have destroyed Gamilus, thus proving themselves no better than their enemy. Kodai smashes a gun against the deck, shouting, "victory tastes like ashes!" Such drama would probably have been lost on the target audience.
After the Yamato destroyed the Gamilon base on Pluto, the Gamilus fleet attacks. The American series shows Colonel Ganz shouting, "We're going to crash into them!" as if this was not what he wanted. In the original Japanese dialog, Schultz tries to ram into the Yamato, kamikaze style, shouting "Desler Soto banzai!" (Long live Lord Desler!)
Several scenes showing Japanese "honor" were translated into much less powerful English. Many scenes involved doing something because the person was honor bound to do it, where the American translation just made it look like the right thing to do.
There are many scenes showing the typical Japanese discipline in the ranks. When the Yamato is caught between energy absorbing gas and a red star, they are almost swallowed up by a huge solar flare. Okita orders Kodai to shoot the flare with the Wave Motion Gun. Kodai questions this, to which Okita shouts, "Do not question my orders!" In the English translation, Captain Avatar merely says, "Repeat the order." In another episode, Avatar slaps Wildstar for acting without orders, but this is made to appear that the Captain is merely lashing out to cover the pain he feels from his radiation sickness. In the original version, slapping a subordinate around for disobedience doesn't seem to require explanation. This is also shown in "The New Voyage," when Kodai smacks Sakamoto for showing off.
In the Japanese series, Dr. Sado was shown as a drunk, but this was masked out of the US version. That spring water the Doctor was so fond of was actually sake.
When the Yamato crew captures a Gamilus pilot, Kodai pulls a knife on the pilot and tries to avenge his parents' death. The Gamilus pilot grabs the knife and tries to kill himself. The entire knife portion of the scene was removed from the American series.
During the Yamato's attack on Gamilus, Hisu demands that Desler break off the attack. Desler's response is to shoot him. In the US version, the shooting scene is removed.
The Comet Empire - Original versus Remake
The original movie, "Farewell to Space Battleship Yamato" was rewritten to allow for the series known as "The Comet Empire." Most noticible was the survival of the crew - in "Farewell," many of the crew members are killed off in some way - Yuki is shot on the bridge of Desler's flagship and later killed in a bridge explosion, Kato and Yamamoto are killed in battle, and Kodai rams the Yamato into Zordar's juggernaut. The re-made version lets almost everyone survive, including the ship, as Teresa (Trelena) steps in at the last minute and destroys Zordar.

Some other noticible differences:

There is no "Andromeda Fleet" commanded by Captain Hijikata in the original movie. Hijikata, the man known as Gideon in the English series, is actually rescued near the Eleventh Planet, and takes command of the Yamato. The Battle at Saturn is a lot shorter in the original movie as well.
A cool new weapon, the Dissemination Wave Motion Gun, never makes it into the re-done series.
Desler doesn't get as many scenes in the original, but his maniacal nature is much more evident. In the original movie, he has the help of the Comet Empire fleet, which he destroys in an attempt to shoot the Yamato. In the series, not only does he have more screen time, but he ends up having to escape imprisonment by the Comet Empire, and ends up befriending Kodai instead of committing suicide at the end.
The method of destroying the White Comet is different. In the original, the Yamato fires the Wave Motion Gun at the Spiral Core. In the series, both Gideon and Desslock say to shoot at the unprotected bottom of the Comet City.
Teresa/Tralena is given a much different role. Instead of being a mere prisoner, she is the lone survivor of a planet she accidentally wiped out with her mind energy. She falls in love with Shima (Venture) and saves his life at the end.
The Bolar Wars
The English dubbed version had two inconsistencies - first, Desslock's aide, General Talon, was called Sergeant Masterson in an obvious continuity error. Second, there are references to Desslock and the Star Force fighting the Comet Empire together. In fact, Dessler helped the Yamato with battles against the Black Star Cluster Empire. Since, at that time, there wasn't much chance of the average American viewer having seen "New Voyage" or "Be Forever Yamato" and knowing about the Black Star Cluster Empire, it was attempted to make it look like the Black Nebula Empire was a part of the Comet Empire, and that Zordar was not the supreme ruler of the empire.