Not with My Sister You Don't - S1-E19
Character mistake: Howard Borden goes to Bob's office and says it's the first time he's been there. In fact, he had come to the office to address Bob's "fear of flying" group in the first episode.
Fly the Unfriendly Skies - S1-E1
Continuity mistake: When Bob talks to his friend Howard about flying, Howard's hands move from resting in his jacket pockets to his hips between shots. (00:04:50)
I Owe It All to You... But Not That Much - S1-E13
Visible crew/equipment: When Bob and Howard enter Jerry's apartment, set lighting is visible at the right. (00:17:00)
Emily, I'm Home - Emily? - S1-E21
Continuity mistake: Emily has her hand in the cupboard putting the groceries away. The shot changes and it isn't.
Not with My Sister You Don't - S1-E19
Continuity mistake: When Mr. Dabney is yelling at Carol she is holding a pencil ready to write. The shot changes and she's no longer ready to write.
Continuity mistake: Bob hands Margaret the petition, and she is holding it away from her body. The shot changes and she is now holding it against her body.
Anything Happen While I Was Gone? - S1-E10
Visible crew/equipment: When Cynthia leaves Bob's office, a crew member can be seen by Bob's desk. (00:06:25)
Let's Get Away from It Almost - S1-E15
Continuity mistake: About 2/3 into the episode, Bob pulls out his suitcase to start packing, sets it on the bed and opens it. After being interrupted by their neighbor the scene moves back to the bed where the suitcase is closed again even though no one has gone near it.