Plot hole: The only reason the terrorists' plot can work is that the airports around Dulles are all closed to landings because of the violent snowstorm. If there were no storm, the pilots of the airliners in the holding pattern would simply divert to nearby airports when they started running low on fuel. If they were able to do that, the whole plot would simply fall apart. How were the terrorists able to count on the storm happening on the very day General Esperanza's flight was due to land? They didn't have any influence over the date of his flight. How did they know the storm would be so bad that all airports would be closed - except Dulles? I don't think they had any way of predicting the weather quite that accurately, and If the storm hadn't hit or had been even slightly less severe the pilots of the stranded airliners could easily have diverted to any one of half a dozen alternate landing sites, including a nearby Air Force base. They could do this without consulting or even contacting air traffic control. The whole plot falls apart from there - no hostages, no leverage, and who cares what happens to the people on Esperanza's plane? They'd have it shot down as soon as they knew Esperanza had killed the pilot and taken over the flight.
Plot hole: The whole of Col. Stuart's plot to free General Esperanza and flee to a country with no US extradition laws would be rather impossible, as the plane with Esperanza and the terrorists would have been brought down by the US Air Force long before reaching international waters, especially given the fact that they would not maintain control over the airport landing systems after taking off.
Plot hole: When they try to contact the planes using the air phones, they say there are 18 planes but only 5 have airphones, and they got through to 3 of them, but they're trying to contact the others. Nothing the terrorists did kept the planes from talking to each other, so there is really nothing keeping the informed planes from radioing the information to the other pilots. (01:04:00 - 01:04:50)
Plot hole: At the beginning of the film, it is still daylight, which at Christmas, would mean it's about 4:30pm at the latest. The whole incident of the film lasts around 4 hours (figured by the scene when Barnes was talking to the planes and said the trouble started around 2 hours ago coupled with the fact that not long before that, Trudeau confimed that Holly's plane had only 90 minutes worth of fuel left). So why at the very end are there shots where it appears the the sun is rising in the distance? (And no, it's not caused by the fire of the exploded plane. By that reckoning, the terroists would have had to have taken over the airport well after midnight, which is pretty much impossible since Esperanza's plane was already on route.) (00:00:35)
Plot hole: When McClane gets kicked out of the control tower and is sent down in the elevator with Coleman he quite obviously stops the elevator before saying "Here's a couple of words, F**k off." to Coleman. He then opens the top panel and climbs out WITHOUT restarting the elevator. Almost as soon as he has closed the panel again the elevator has reached the bottom and the cops are asking "Where's the other one?" As it is meant to be a single shot and there is no delay we know Coleman did not start the elevator again herself. (00:38:25)