Factual error: A force of Russian Tu-22 Backfire bombers attacks the aircraft carrier USS John C. Stennis (CVN-74) by sneaking in under the ship's radar. This is all well and good except that carriers usually don't use their own radar, they have Airborne Early Warning aircraft (E-2 Hawkeye's) that can see much further and not give away the carrier's position (let alone the F-14s which would be patrolling too) not to mention the fleet of destroyers other ships guarding the carrier. The whole point is, the US Navy practiced and planned for such a "carrier versus Backfire" battle for years. I guess in the interest of furthering the plot Hollywood has to ignore the immense measures the USN takes to protect those multi-billion dollar assets, not to mention the 5000+ sailors that man them.
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.
Factual error: The Israeli A-bomb was dropped "at the Golan", yet, the landscape where it is found looks like a sandy desert, and as time flies the bomb is completely covered with a sand dune. The Golan has everything but sands or dunes. The terrain over there is magmatic, rocky and mostly black, as the Golan was an active volcanic area. Had a bomb fallen from the sky, it would most likely remain on the ground, smashed.
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.
Factual error: Why is the President's motorcade so small? There were only a few cars there to protect the most powerful man on the face of the Earth. The President ALWAYS travels with over a dozen Secret Service vehicles, to protect him. Even if when he left the Superbowl was an emergency, all of the motorcade would have left with him also, ruling out the possibility that only some of the cars left with him.
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)
Factual error: After the US President gives the order to launch the missiles, you see a view of a missile preparing for launch. This is followed by scenes of B-2s launching. The missile shown is an older liquid fuelled missile. The US military retired all liquid fuelled missiles from its inventory long before the first B-2 rolled off the assembly line. As such you wouldn't see both in use at the same time.