When Regis first pulls up to the White House, he is parked in front of the large metal gates. When he shows the security guard (secret service?) his ID, you can clearly see that there is no gate and the plastic bar (seen previously inside the large metal gates) is directly in front of his car. The next scene is him pulling up to the spot he was just in.
When Regis retrieves the newspaper from the front porch, it is folded over. When he opens it up on the kitchen table to find the picture, the paper isn't folded anymore. Also, neither the newspaper nor the manila envelope show any signs of having been creased.
When Det. Regis meets Kyle at the park, the gun he removes from Kyle's coat has a silver barrel. When the detective returns Kyle's gun to him, the gun is entirely black. It is clearly not the same firearm.
When first arriving at the crime scene, Det. Regis is directed to go down the short hall and turn left. Yet the room he enters is down the hall and to his right. The spoken directions would have been essentially correct if they had been issued one hall earlier.
When the lab tech prints out the blown-up picture of the secret service agent's head, the image has a black border like the edges of a negative. If the image were really blown-up and cropped, there would be no border visible.
Watches (timepieces) are featured several times throughout the film to establish time line. All of the watches shown worn by multiple characters are made by Raymond Weil, a luxury watch brand. It's very unlikely that civil servants would be able to afford the watches on their salaries.
Halfway through the investigation, we are told that the murder victim's date book has a forged entry about meeting with a "tell-all" publisher. A police detective would have verified the appointment with the publisher and its topic long before the forgery was revealed, saving days' time in the investigation.
What is supposedly the leg of Detective Regis as he is standing on a ladder discovering a hidden microphone in his apartment, with Detective Stengel next to the ladder, is a single leg on the ladder's paint can platform, not a ladder step; the platform couldn't support the weight of a person.
Near the end of the movie where Nina Chance waits for the secret service to arrest her in the tunnels, she runs up a flight of stairs and attacks an agent. Clearly this is a stage built as the walls are wobbling during the action scene.
The goof items below may give away important plot points.
In the scene in the Oval Office where Alvin Jordan demands the President's resignation, there is a painting on the left wall when we are looking at the desk. In some shots there is a spotlight on it, in others it is dark. The painting on the right side is consistently lit through the scene.
When Nick Spikings is murdered at his house, one of the shooters enters through a window. When inside the house he draws a semi-automatic handgun. It is clear that the slide is locked back, which would indicate that the weapon is empty, yet he fires it in a shootout seconds later.