Tony's crutches appear and disappear between shots.
Tony Almeida's ankle suddenly gets better when he talks to Ryan Chappelle about Jack coming in.
Jack mentions "Mr. Palmer" to Mrs. Palmer, which was meant to convey that Palmer had been removed from office by the Cabinet vote. Although Jack very well might have referred to David Palmer incorrectly as Mr. Palmer, he was actually still the president and should have been referred to as President Palmer. The Cabinet only voted to temporarily appoint Vice President Stanton as "Acting President" (the exact term used in the 25th Amendment) due to the Cabinet's judgment that Palmer temporarily was "unable to discharge the powers and duties of his office." Only Congress through the impeachment process can actually remove a president from office. Even then, afterward he would still referred to as President Palmer. The custom is for all former presidents, governors, Cabinet secretaries, etc. to be referred to by their highest-ranking title for the remainder of their life. Jimmy Carter is still referred to as President Carter, despite being out of office for 35 years. Note that in official settings, such as in the 2016 primary debates, Hillary Clinton is referred to by her highest previously held office, Secretary Clinton.
After fleeing to the attic, Kim would not have been able to fold up the ladder and close the hatch from up there. These attic hatches with folding ladders are not designed for that, there is no kind of strap attached and she did not have time to tie a string to it or anything.
In the credits at the beginning Billy Burke is written as "Billy Gurke".
Kim would not have been allowed to enter the Matheson's house without a police supervisor.