Dr Lily Sinclair's stockings repair themselves at least twice during the escape sequence at the end of the film.
As they are lifted out of the shaft, Eddie and Dr. Lily are covered in white ash, but by the time they climb out of the bucket all the ash is gone.
When Shannon leaves his house for the meeting at C-Systems, he leaves in a Cadillac Fleetwood Sedan. When he arrives at the meeting, he arrives in a Lincoln Town Car.
When Eddie is hanging from the lift at the end of the movie, Lily is supposed to be in the lift. However, one shot shows no one in the lift. At the same time this goof happens, Lily is actually heard saying, "Hold on Eddie!"
In one scene, while Rachel and Keanu are running through the planetarium, Rachel's coat was zipped, then unzipped, then zipped again.
At more than one point in the film, hydrogen is produced and seen to burn with a luminous yellow flame. This is incorrect: a stream of hydrogen burnt in air has an almost invisible flame with perhaps a slight trace of blue. Admittedly, this wouldn't show up very well in a film.
Condolences are received from the British "Royal Academy" on the death of Dr. Alistair Barkley. The "Royal Academy" is an Arts institution; perhaps the writers' meant the "Royal Society." (Founded in 1660, the Royal Society is the independent scientific academy of the UK, dedicated to promoting excellence in science.)
Chicago River bridges don't open for tour boats. They only open for tall masted sailboats in daylight hours during specified mass movement periods in spring and fall. Tour boats almost never go out on the river during the winter.
Near the end Eddie and Lily are in the lift cage which is violently blown out of the shaft and then falls back down from a considerable height until stopped very abruptly by the cable. This would have either killed or seriously injured them same as if they fell from that height to the ground yet they appear unharmed.
Eddie's sliding down the steel grating on the lift bridge should have shredded him like a cheese grater but there's not even a scratch on his jacket.
All scenes with hydrogen flames: hydrogen flames are pale blue and almost invisible. Yellow flames are due to burning carbon (soot). This suggests methane (or another hydrocarbon gas was used for the effects)
The explosion that destroys the steel mill occurs in "stages" which is not how it would happen. Eddie is shown riding away from an explosion which expands slowly enough for him to do so, rather than all at once as it would. He would have been thrown from his motorcycle or hit by debris and killed.
Virtually every action movie and series has had its share of heroes run as fast as they can and try to leap behind shelter, just as it explodes.
When Eddie and Dr Shannon are talking and the FBI are listening Dr Shannon hits a scramble button so they can't listen. Eddie does not have a descrambler so they could not have talked about where they were going or what they were going to do.
When the cops (FBI Agents) are chasing Eddie in downtown, after he and Lily leave the Hyatt Hotel, Eddie runs toward a bridge. While he gets off the bridge, he slips under a truck. When he gets up to run away he is covered in oil and other gook. When he finally runs over to Lily in the cab he's completely clean.
When the cable to cage that Eddie and Lily are riding up to escape C-Systems breaks the cage is violently tossed back and forth in the shaft, but in to close ups they don't move at all in relation to the cage. If this really happened they would have been tossed around inside the cage or even ejected.
During a test of the hydrogen fusion device early in the film a shot of the monitoring software on the computer is shown. Amongst the information displayed is the "Torus Radius" of the fusion device. A torus (a donut shaped ring) would be appropriate for fusion research, but the device shown in the lab is not a torus.
As Eddie is fighting the last goon some gray pipes are knocked about, making a metallic ringing sound, yet the pipes are clearly flexing. This is because they are actually lengths of gray PVC electrical conduit.
An actor filmed a scene saying the words "...a disturbance at the Smithsonian" but the words "science museum" were dubbed over Smithsonian instead. Since the museum was supposed to be a fictitious place, they couldn't very well call it the Smithsonian.
In the shot taken from the top of the drawbridge looking down after the cop/stuntman has slid down off it you can see the landing pad quickly pushed out of view by the actors at the bottom.
As Eddie and Lily are running away from the trooper along the roof of the observatory the tail of the sniper helicopter is visible but there is no chopper sound. But then in next view from that angle the tail is no longer seen.
At the drawbridge scene, you can see the officer slide down the bridge and the next scene the cops are hiding the landing cushion.
National manhunt for Eddie, yet he refuses to disguise himself or cover his obviously noticeable hair style with a hat when on the run.
At the beginning of the film, there is a lecture hosted in a university building being attended by numerous scientists. Despite all involved likely being brilliant individuals, the very prominent banner hanging over the stage misspells the word "millennium" (omitting the second "n").
When Eddie asks Lily where she lives, she replies, "Kimbark and 54th". However, when he drops her off the street signs clearly show they are on Ellis and 48th.