Continuity mistake: Just before George withdraws some blood from Bex's arm, her right sleeve is rolled up when Addison is beside her talking. In the next shot as Bex is drawing, the sleeve is suddenly rolled back down and George pulls it back up again to get some blood.
Owner of a Lonely Heart - S2-E11
Continuity mistake: When Dr. O'Malley is talking with Carl Murphy in his room, the position of the circle of containers (with the leeches inside them) changes between the shots during the scene. (00:32:10)
Owner of a Lonely Heart - S2-E11
Visible crew/equipment: When Burke hands Cristina the cup of coffee as she leaves for the hospital, blue screens can be seen in his eyeglasses.
Thanks for the Memories - S2-E9
Continuity mistake: When Holden is talking to Meredith about whether he wants the surgery or not, his hand is on this chest, then isn't, then is again. (00:28:10)
Audio problem: When Derek shouts over the second floor banister to Weiss, Weiss walks over to the staircase and says "Derek, I've been looking for you," yet his mouth doesn't move. (00:05:40)
Continuity mistake: When Christina removes the beak from Stu's leg and has it on the end of a pair of tweezers, she shows it to George so that it is pointed at him. In the very next shot the beak it pointed at her. (00:08:20)
Continuity mistake: When Alex and George are trying to get out of the elevator that they are stuck in, watch the monitor screen attached to the gunshot victim. The lines on the monitor keep instantly changing appearance (from straight, to jagged, and then back, etc.), especially the middle blue line. (00:13:05)
Continuity mistake: When Meredith, Christina and Izzy are standing by the hospital hall balcony talking, the nurse, doctor and patient extras walking and passing in the background are inconsistent from shot to shot. In addition, the position of the three ladies arms / hands on the banister keeps changing during this scene. (00:12:35)
Continuity mistake: When Alex walks over to the desk that Derek is sitting behind, with the couple arguing in the background, there is a box of tissues with a tissue pulled so that it is almost out. In the next shot the tissue is barely out of the box. (00:26:20)
Continuity mistake: When Addison shows up at the end of the episode, the umbrella she holds keeps changing position and swapping hands between shots. (00:42:05)
Character mistake: Christina pronounces the dead patient's condition incorrectly. She says Haemotomachrosis. The condition is Haemochromotosis.
Continuity mistake: Izzy tells the male patient she is a good doctor even though she was a model. Her hair is parted to the left and in the next shot it is parted to the right.
Continuity mistake: Arizona is wearing fitting black slacks and black heels and has two legs (not a prosthetic on the left). (00:37:45)
Other mistake: The exact same shot of Derek's radio tuner is used twice-once when he calls Amelia and again when he gets in the car after helping at the accident. Both times, the clock says 7:45PM, but Alana (the AP class taking, cello playing student) says that she's supposed to be at school, implying it's sometime between 8AM-ish and 3PM-ish. Also, the sun sets around 7:30PM in Seattle on March 26, but it is obviously day time for the duration of this scene so there's no way it could be 7:45PM in either of the shots in which the clock is shown. (00:03:30 - 00:18:40)
Other mistake: When Derek has finished showing Callie and Arizona the picture of Cristina getting her nomination, he leaves to take the kids into what we are supposed to believe is daycare...however the sign on the door reveals it is a dispensary. (00:02:30)

Visible crew/equipment: After Meredith discovers Derek visiting her mother at the nursing home, when it cuts to Miranda in the OR the T-mark can be seen on the floor at Cristina's feet. (00:26:40)

Owner of a Lonely Heart - S2-E11
Visible crew/equipment: In the NICU, when George starts boasting that he has the best quint, in the overhead wideshot we can see the T-mark (greenish yellow) on the floor near Kate, moments before Karev walks in and stands there. It's visible again just as Karev walks away. (00:01:05)
I Always Feel Like Somebody's Watchin' Me - S6-E3
Continuity mistake: When Alex is giving Izzy her medication, he is holding a water bottle and an unpeeled banana In his right hand. Then the banana magically disappears and he is holding only the water bottle. Immediately, the banana reappears and it is now peeled. This all takes place in three quick shot which are from different takes.
Factual error: Derek performs CPR on Meredith in the back of the ambulance, but he does so incorrectly. He gives one breath and five compressions instead of two and thirty. Also, drowning victims need oxygen, and Derek should have used a BVM to ventilate Meredith, not mouth to mouth. Any doctor would have known how to provide proper treatment.
Factual error: Izzie tells her patient, Cheyenne and her mother, Mrs. Ward that they live in the same town she grew up in - Chehalis, Washington, yet mispronounces it. She says CH-halis (like CHurch) when it is SH-halis like Chinook Salmon.