Continuity mistake: In the scene on the NAOC (National Airborne Operations Center) E-4B where the plane begins to shake, everything on the conference table, including books, maps, charts, etc., is moving, with the exception of a clear cup of what is supposed to be soda. Not only does the cup not move, but the liquid in the cup (which is most definitely not liquid but plastic) does not move either. It's glued to the table.
Continuity mistake: The nuclear blast blows in the windows at the hospital where Cathy works and all the medical staff is showered with the broken bits. At the end of the movie Cathy doesn't have a mark on her. Even if it is safety glass, the small pieces would still leave nicks, scrapes and small cuts on exposed skin.
Continuity mistake: When Ryan's helicopter crashes to the ground and rolls over, the pilots are thrown partly from the cockpit of the helicopter. When it finally comes to rest, there is a pilot hanging out of the cockpit window. Approximately three minutes later, when Ryan struggles out of the helicopter door, the cockpit window is now empty. (01:07:10 - 01:10:40)
Continuity mistake: The President is told the missile launch sequence will take 30 minutes. When he gives the order to begin the sequence, you see B-2 bombers launching from bases in Italy. A short time later a Russian staff member reports the B-2's somewhere over Poland, however the missile launch sequence still hasn't completed. B-2's are not fast enough to go from Italy to Poland in under 30 minutes.
Continuity mistake: When Clark pulls the radiation indicator off the dead scientist, the readout is 7.0. The very next shot is a screen shot of the readout now displaying 6.9. Unlikely the plutonium was decaying that fast, or the bomb would not have been as potent...
Continuity mistake: At the end of the film, the American and Russian Presidents are making a speech at the White House. The medium shot shows the audience seated directly in front of the podium. When you see the wide shot later, there is an aisle that goes straight up the middle to the podium, where nobody is seated. Strangely, it looks like the entire presentation in front of the White House is digitally added (like Forrest Gump). Couldn't they easily match the medium shot if they are creating it later?