Other mistake: In the two scenes that occur at Lucky's base in Iraq, it is quite obvious the writers did not do much research about the Army in Iraq now, or the Army in general. Alcohol is not allowed on any US base anywhere in the Middle East during the current conflict, and this is true for all branches of the military. Even if Lucky did manage to procure contraband alcohol, he would not drink it openly, because an MP would arrest him within minutes. If he appeared in his Sergeant's tent drunk, he would be arrested, and severely disciplined, probably demoted. No one on a US base would be known as a habitual drunk, because anyone found drunk more than once would be either sent back to the states for rehab, or dishonorably discharged. Also, in the US Army, Sergeants are never addressed as "Sir." This is one of the very first things a new recruit learns at Basic Training, and it is drilled into him. It is extraordinarily unlikely that a soldier would slip up and call a sergeant "Sir" once, let alone repeatedly, as Lucky's buddy does. After the first time, the Sergeant would correct him.
I Married a Mind Reader - S1-E11
Factual error: A nitpicking mistake, but on the set of "I Married a Mind Reader", the front door is a modern steel design. Back in the 60's, front doors were almost always wood (steel doors weren't available until the 1970's or 80's), and the window design would have been larger on a 1960's fan-window wooden door.
Penny for Your Thoughts - S1-E15
Revealing mistake: In the first scene the clock shows an impossible configuration. The hour hand is slightly before the five, and the minute hand is between one and two. If it's about seven minutes after the hour, the hour hand should be slightly past one of the other numbers, not slightly before it. (00:00:24)
Suggested correction: Not sure if this is technically a mistake or not. These clocks run on batteries, and when the battery's time is almost up (no pun intended), the weight of the hands sometimes over-rides the battery's strength to move them properly. This is likely a dying battery that failed to move the hour hand correctly. So while it is 'a mistake', it's part of real life, and not really a 'mistake in the episode'.
In Sickness and Adultery - S1-E5
Continuity mistake: While in the park with her boss, Allison's hair keeps moving between behind her back and in front of her shoulders.
Continuity mistake: When Allison is in the bath we see her surface and wipe her hair. In the shot from behind her hand is raised, and in the front it's lowered. (00:08:30)