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.]
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: When Rory asks Lorelai to call Emily to get her out of Friday night dinner so she can celebrate her and Dean's 3-month anniversary, a boom mic drops into the shot as Lorelai stands to get the phone. (00:07:05)
$35K O.B.O. - S1-E18
Continuity mistake: In one shot Grissom puts a shoe on its side with a pencil. In the next shot the shoe is upright again.
Revealing mistake: When Max is holding Lydia upside down from the window, in one shot of Max you can see the harness used to hold Lydia.
Snow Place to Go/Dunce Upon a Time/Gems the Breaks - S2-E4
Continuity mistake: Dunce Upon a Time: When Nutty shows the beans to Giggles, she takes the purple bean out of his hand. Then right before Nutty eats the beans, the purple bean is back in his hands, and in the next shot, it's in Giggle's hands again. (00:08:24)
Jane and the Truth Snake - S2-E5
Continuity mistake: When we first see the guys at the pub, Jeff takes a swig of beer and you can see that his glass is almost empty. After a few seconds of conversation, he takes another sip and the amount of drink has significantly increased. (00:06:00)
Dad's Dead - S1-E2
Continuity mistake: In Titus' first flashback, he and Dave sit on a couch in Ken's peripheral vision. When the camera shifts to the "fist cam", the couch is now facing Ken head-on. (00:02:15)
Character mistake: There is a spelling error in the newspaper that Sakurako Sawatari is reading in one episode: the word, "admits" is spelled "adwits." (00:01:00)
Continuity mistake: Larry is sitting on the couch close to the arm, drinking wine. Susie sits down, making Larry spill his wine on the couch. Larry is now sitting in the center of the couch. (00:11:49)