Continuity mistake: When Shirley walks through the door you can see over Alan's shoulder that he's reading the comics in the daily paper. As they talk the paper changes to the business section.
Revealing mistake: When Denise is showing Brad how to kiss, the first kiss is a typical "stage kiss" with their lips pretty clamped shut, but she then details what he's doing wrong with his tongue, which clearly wasn't at all involved with the sort of kiss they just shared.
Other mistake: As Denny asks "did she sleep in your room?" Alan leaves Denny's hotel room, pulling the door behind him. The swinging door catch is in the closed position, sticking out from the door frame which would prevent the door from being able to shut - the shot cuts a fraction before impact and we hear the sound of the door closing anyway.
Hired Guns - S1-E10
Continuity mistake: As Denny walks out of his office after shooting the assailant, Sally moves to the doorway, hands by her sides. Shot cuts to further away and her hand is suddenly up by her mouth. (00:32:40)
Character mistake: Lorraine mistakenly tells Denny to "call 999" instead of 911, and when asked about it by Katie, denies having ever spent time in the UK (later revealed to be a lie). But this isn't some high-pressure slip of the tongue, she's highly intelligent and has been in America for a decent length of time, is working hard to maintain her facade of being born and bred American, so there's no way she'd slip up over such an obvious thing.
