Lost (2004)

Abandoned - S2-E6

Revealing mistake: As several camera angles show, Sawyer's makeshift stretcher was made by drilling multiple holes in the upper frame struts, through which was threaded rope made from dried roots or vines. The cast who supposedly constructed it were not carrying power drills among their primitive implements.

The Other 48 Days - S2-E7

Revealing mistake: When Goodwin and Ana Lucia sits down to have a break and Goodwin hands over some fruit to Ana, she says "Where do you think they got it? I mean they're not even wearing shoes", directing to the knife. If you watch in the background you can see a car driving.

Mortug

The Long Con - S2-E13

Revealing mistake: When Jack asks Locke for the vault combination he yells "Jack" (his own name) instead of "John". (00:01:55)

One of Them - S2-E14

Revealing mistake: When Sayid and Locke are talking to Henry Gale in the hatch, just as Jack comes in and finds them, the front part of the arrow supposedly piercing Gale's shoulder is at a different angle to the back part. This is visible in a number of shots.

STP ★

Dave - S2-E18

Revealing mistake: In Season 2, Episode 18 - Dave: When Ana Lucia is threatening "Henry Gale" in the hatch cell; every time he moves and his makeshift shirt slips, you can see a line on his right upper arm where they applied make-up. Apparently he's wearing makeup on all the exposed parts of his face and neck to make him look sunburned, exposed to the elements etc. This is not just a normal suntan line, as his shirt wouldn't normally fall down that much out in the open and he's been inside for days now.

Live Together, Die Alone, Part 2 - S2-E24

Revealing mistake: After Sawyer has been shot with the syringe thing (I'm not sure if Kate had been shot yet) Jack fires his gun five or six times into the jungle. The last few times he fires it there is no flash or any indication that the gun has been fired.