Half way through the Battle of Hoth mission, you (playing as Luke) get shot down, and finish out the mission as Wedge Antilles. Yet you continue to fly in the same Snowspeeder you were in earlier, with the same amount of damage and everything.
TIE Interceptors appear in early missions of the game, long before they were "invented" in the Star Wars universe.
The "before mission" descriptions of the ships say that the X-Wing is "the fighter that killed the Death Star." Even if you play on the first mission, before it has been destroyed.
There is a glitch in the final level that, just as you enter the Death Star's core, your craft can only fly very slow.