The shorts on Amy's tights disappear in some shots.
The rope on the handle of the Clone-O-Mat changes to a chain the second time Farnsworth pulls it.
The characters stand right next to the magma (Amy and Leela even sit on the rim) without getting hurt; in reality, even approaching within a few yards would burn them severely.
During the final cloning scene prior to the last flashback of Seymour waiting for Fry, both Amy and Leela revert to their usual clothing instead of the wrestling outfits they were wearing earlier.
However after Bender emerges from the lava with Seymour (where Amy and Leela are still in their wrestling gear and Fry is in his underpants), there is a cut to outside the Planet Express building before going back in, and since Fry has redressed since then too it's possible that a few minutes passed and they merely got dressed again, considering neither Bender nor Seymour are covered with lava either.
The score of the Rose Bowl was reversed in the game, Stanford was leading 9-3 at halftime in the actual game.
Fry's assumption of how long Seymour lived after Fry was frozen seems based on an assumption that Seymour was 0 when Fry met him, however, this is never firmly established.
However, the montage at the end of the episode seems to confirm this.
It is possible that since Fry would not have known Seymour's age when he found him, nor had a way to find out from what we're shown, that he simply counted the time from when he got Seymour. It's also possible that Fry considered meeting him to be his "first birthday" as Seymour Asses.
When Bender enters the lounge with Robo-Puppy, he is holding him on a leash, yet after he says the line "Of course, after he goes you have to refill the canisters.", the leash completely vanishes.
It is possible it's a retractable leash, since it's a robot dog.
The lava reflected Fry's image like water, in reality lava does not reflect.