Rendezvous with Yesterday - S1-E1
Character mistake: When Tony talks to captain of Titanic he states he was born in 1938, but in episode 4 "The Day the Sky Fell In" it is December 1941, he should be 3 years old, but as a young child he is about 12 years old.
Character mistake: Lt. Joey said to Lt. Sulu "You don't outrank me and you don't have pointed ears" but Joey is a junior grade lieutenant so Sulu would outrank him.