Other mistake: When the stormtroopers break into the control room, the stormtrooper on the right of the screen hits his head on the door frame. On the DVD release they've added a thump when he hits it.
Continuity mistake: After Darth Vader kills Ben, there's a shot from the docking bay towards him. Vader's lightsaber is missing its red color. [This has been fixed in the 2004 DVD, but is still valid for VHS prints.]
Luke: How did my father die? Obi-Wan: A young Jedi named Darth Vader, who was a pupil of mine until he turned to evil, helped the Empire hunt down and destroy the Jedi knights. He betrayed and murdered your father.