Continuity mistake: Elizabeth walks away from the security brief and puts her arm on the wall. When David approaches her, her arm is still on the wall. When the camera changes to the front angle, her arm is not on the wall any more. This is an instant cut. (00:06:30)
Visible crew/equipment: Just after Kevin is executed, you see the assassin walk off to screen left. However you see movement in the rear view mirror of the car on the far right hand side of the screen, evidently a crew member since everyone has been killed. (00:27:15)
Other mistake: When Jack sits down in room 2, his watch says 2:50, despite the time being 1:05. His watch is correct in other scenes so it's not that it's set wrong or broken. (00:05:00)
Audio problem: When Jack and Rick are talking in the water tower, a lot of the audio in that scene is either out of alignment or overdubbed. Easiest to spot is when Jack is checking Rick's wound. (00:10:30)
12:00 Midnight-1:00 A.M. - S1-E1
Continuity mistake: Kim Bauer has a full set of glittery pink disco nails on episode one (midnight) but then these are not visible at all in most episodes. In the 2pm episode her nails look clean/natural in nearly all the shots, apart from during the phone call with Rick where traces of pink glitter can be seen. I know she's had a very rough night but it doesn't explain the amount of damage her nails have sustained.
Day 3: 7:00 P.M.-8:00 P.M. - S3-E7
Character mistake: At 07:03:05 PM the man pointing the gun at Jack is right-handed, but he aims with his left eye, which is his weak one. He keeps his right eye closed as he walks away and no longer needs to aim, which is a dead giveaway he has never used a gun before.
12:00 Midnight-1:00 A.M. - S1-E1
Character mistake: When Jack subdues Mason he proceeds to check his pulse to check Mason is still alive. When taking the pulse however Jack uses his thumb. This is not how a pulse is checked, as the thumb has it's own pulse and would therefore give Jack's pulse instead of Mason's. Being ex-Delta Jack would know this and not make the simple mistake. (00:22:10)
11:00 A.M.-12:00 Noon - S1-E12
Character mistake: When Jack mentions the siege at Waco, he implies that the ATF's raid failed because an agent on-site screwed up. Their plan had actually been shot before the assault team even reached the compound; a reporter inadvertently compromised their advantage of surprise when he got lost and asked David Koresh's brother-in-law for directions, providing the Branch Davidians ample time to arm themselves in anticipation of self-defense.
11:00 P.M.-12:00 Midnight - S1-E24
Other mistake: As David is walking away from Sherry, there is daylight flooding into the ballroom, just 20 minutes before midnight. (00:32:30)
Audio problem: When Jack is getting suited up, the new bloke arrives and we hear him put his case down on the glass desk. Camera changes and we see him put the case down on the desk a second time. (00:12:50)
Suggested correction: You can see George (replacement to Alberta) holding 2 briefcases just before Jack sits down to put his shoes on.