Continuity mistake: In the scene where Murdock is in jail talking with Emma on the phones through the glass, he presses his fingers to hers, against the glass, & the glass shatters. Right when it is shattering & he pulls away, if you look very carefully you can see the reflection of his hand in an additional pane of glass that is still there! The next shot shows no glass as they kiss, but when the original glass breaks, there is still a pane of glass remaining, as evidenced by the reflection of his hand.
Continuity mistake: Murdoch has to break in a window to escape from being crushed by a building. The first scene shows him kicking in the window with many jagged pieces at the top of the window frame. Another scene then shows Murdoch still removing the glass, but now there are only two smooth fragments at the top of the window. We then see Murdoch moving his head through the window and entering into a room with no glass at the top of the window frame. All the while, during those three quick scenes, there was no effort by Murdoch to clear the broken glass at the top of the window.
Revealing mistake: When Murdoch is flipping through the phone book looking for Karl Harris, the names are nonsensical (Mreland, Mrons, Msaac - i.e. names that start with I starting with an M). Secondly, the pages are all the same. Thirdly, if he is looking for Harris then he should not be flipping forwards through the Ms (or even the Is), he should be going backwards.
Continuity mistake: When John falls down after reading the newspaper clippings in front of the Shell Beach billboard, one of the Strangers can be seen approaching him on the far left of the screen, in front of a window at the top of some stairs. But in the next shot, the Stranger is suddenly further down the stairs.