Day 2: 3:00 A.M.-4:00 A.M. - S2-E20
Corrected entry: In series one, there is a scene where Jack is changing his shirt in his office, there are some very visible Japanese symbol style tattoos on his biceps. In series two, when we next see Jack's bare arms (when he is being tortured) the tattoos are no longer there.
Correction: I haven't seen the episode where you believe that tattoos have disappeared, but I do recall the tattoos. All the tattoos visible on Jack in any episode of 24 are Kiefer Sutherland's actual tattoos so they will be there from one season to the next. Even the tattoo Jack has in season three (identical to Hector's) is an actual tattoo Kiefer has. He had it done for the show because he wanted it to look consistant.