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: 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: 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.