Continuity mistake: At the start of the lightsaber fight in the hanger all three go through some large doors and into the big generator room. Behind them a set of stairs have appeared.
Continuity mistake: When Obi-Wan runs towards Darth Maul and Qui-Gon he is halfway down the walkway, but when it cuts to Darth Maul and Qui-Gon Obi-Wan is now at the far end.
Continuity mistake: When Qui-Gon and Obi-Wan are fighting battle droids in the Trade Federation ship, Nute Gunray says, "I want droidekas up here at once." As he says this, he turns his head, causing the "straps" hanging from each side of his headgear to hang slightly behind his shoulders. In the next shot from behind, they are hanging in front of his shoulders like they normally do. (00:05:55)