Continuity mistake: When Tommy Lee Jones pops into his local Irish boozer for a pint of what is supposed to be Guinness, it is clearly not a pint, it is clearly not Guinness (flat Coke, more like), and the level of said beverage in the glass fluctuates wildly and out of synch with TLJ's swigging.
Continuity mistake: Near the end of the movie when Kate is in the Jeep careening down the hill, she swerves to avoid rear-ending a late 1980s Oldsmobile Cutlass Supreme, yet in the next shot, the Jeep is moving past a mid 1980s Ford Thunderbird. In subsequent shots, you can see the Thunderbird still behind the Jeep further up the road.
Continuity mistake: After Max is killed, Jimmy Dove is in the hot tub. As he speaks with his wife he fires one shot into the water, then tosses the gun onto the deck. The Glock is shown with the slide forward and the barrel pointed to the viewer's right. When his wife leaves moments later, without anyone touching the pistol, it is shown with the slide locked to the rear and the barrel pointed to the viewer's left.
Continuity mistake: During the scene at Fenway Park, Paul Molitor of the Toronto Bluejays hits a ball. When they show the runner running to first, it is Joe Carter of the Bluejays.
Continuity mistake: When defusing the bomb in the MIT computer lab, the computer monitor shows "16 bytes" before cutting to Jimmy under the table and then "21 bytes" when it cuts back.