Plot hole: When Zach Young's grandfather died, Zach was said to be the sole heir of the fortune. However, Noah Taylor (the grandfather) had a daughter that appeared several times while Mike Delfino was looking for Deirdre. Where was Kendra Taylor while Zachary Young was spending Noah's fortune on dresses for Gabrielle Solis? Why didn't she claim her share? She simply disappeared.
Factual error: When House is looking over his whiteboard of symptoms for the swimming patient, the symptom "Intercranial Hemorrhage" is shown on the board. However, this is an error. The correct term is "Intracranial Hemorrhage." Anything inside the head is referred to as "intra" not "inter." This is a common mistake for laypeople, however the highly trained and knowledgeable Dr. House should not have made that error. (00:31:25)
Visible crew/equipment: After Charles confronts Choi Sung Ho about the candy, Ho explains that he sold it on the black market to buy real food, and when Ho reenters the mess tent through the side door, we can see that outside there's a director's chair, which actors also use, with something printed on its back.
Continuity mistake: When Shepherd Book tells everyone about the electrical nets, Jayne says, "One day you're gonna tell us all how a preacher knows so damn much about crime." Shepherd then turns to leave. But in the immediate close up of him and Mal, he turns to leave again.
Visible crew/equipment: When Dewey yells for Lois because the bow was put on the present, if you look to the left of Lois, you will see a crewmember kneeling down, handing Lois the Red Dress, who is holding a bucket of water. He quickly gets out of the camera's view. [This is on the DVD of the first season. Someone said on the audio commentary that after catching it, they deliberately left it in to see if anyone would spot it. It's still a mistake, but that's why it's there.]