Continuity mistake: When Woody has the landing gear lowered on the burning airliner, only the right main gear comes down. When Pappy warns him that the other gear isn't down, he pulls up and goes around. As the camera pans over the plane, it shows the left gear down, and the right up. Then when Woody retracts the gear, once again the right one is down.
Continuity mistake: When Spencer Tracy takes Katharine Hepburn to the baseball game (about 20 minutes into the film), several plays supposedly from that game are shown. Some of the plays take place on a diamond that has a well manicured dirt path from the pitchers mound to home plate, while others take place on a diamond with an all grass infield and no path.
Visible crew/equipment: In the final musical number "Strictly off the Record", you can clearly see the shadow of the microphone boom during part of the number.