Towards the end of the episode, just after the Death Star gets blown up, Chris's (Luke's) uniform has the buttons on the front but they aren't colored in & are white for a few seconds. in the next scene, they are colored in again like supposed to be.
During a light saber duel between Obi Wan (Herbert) and Darth Vader (Stewie), Darth Vader uses a red light saber. After killing Obi Wan, Darth Vader is seen with a blue light saber as stormtroopers fire on the Millennium Falcon as it departs. In the next shot that shows Darth Vader, he is again holding a red light saber.
A cloud appears in front of one of Tatooine's twin suns too quickly (possibly a deliberate error since the same thing happens in the actual movie.)
After the light saber duel between Herbert (Obi Wan) and Stewie (Darth Vader), Brian (Chewbacca) and Peter Griffin (Han Solo) run out with the couch. When they are arguing with each other on how to get the couch into the Millennium Falcon, the laser blasts are actually going the wrong way. The stormtroopers are on the right of them firing to the left, but the the laser blasts are coming from the left of them and going right. You can clearly see there wasn't any stormtroopers on the left of them as they were running to the ship.
When Luke is about to destroy the Death Star he turns on his targeting computer. The distance meter (~24,000) starts to go up. It should be going down as he is getting closer to the target.
Han Solo (Peter) is clearly seen taking the couch. He gets it wedged onto the space ship and stands there just holding it because it's stuck. A few minutes later he comes running in to shoot at the enemy. When shooting at the TIE Fighters, you can clearly see the Millennium Falcon no longer has the loading door down with the couch on it as if he pushed the wedged couch off the side to run in and start firing. When attacking the Death Star, Han Solo (Peter) and Chewbacca (Brian) are sitting on the couch firing their weapons as if it was never thrown off their ship.