Corrected entry: When Commander Tucker is transferred from Columbia to Enterprise, the EVA suit he is wearing has the Enterprise mission patch on it instead of Columbia's.
In a Mirror, Darkly (1) - S4-E18
Corrected entry: The U.S.S. Defiant hull number NCC-1764 is incorrect; NCC-1764 is the hull number for the U.S.S. Galina - Heavy Cruiser Class, as listed in the Star Fleet Technical Manual.
Correction: The starfleet technical manual is not canonical. Also, as the entire series is revealed to be a holodeck simulation this could be a programming error.
Only the final episode is a simulation. Riker didn't spend 4 years in the holodeck.
Correction: A quick Google search shows that the USS Defiant has the registry of NCC-1764, as shown in both the Enterprise episodes and the Original Series episode The Tholian Web, where the ship was originally featured.
In a Mirror, Darkly (1) - S4-E18
Corrected entry: At the end of the opening credits for this episode and its sequel, Earth is shown rotating from west to east, the opposite direction as in real-life, likely to highlight the differences in the mirror universe.
Correction: Since they have never shown the sun rising in the mirror universe, the Earth just might rotate west to east. The phenomenom is called retrograde rotation. Venus spins west to east for example.
Correction: That's not really a mistake. Starfleet EVA suits are custom fitted to each crew member and would go with them from duty station to duty station. Considering Colombia is the newest NX class in the fleet, Trip would be extremely busy as the chief engineer getting all her bugs out. He would eventually have changed the patch but it wasn't in his top list of things to do.
Grumpy Scot