When Ed looks at the picture in the hospital, he says "I LUV YOU, out of Caracas. A Panamanian ship.." Caracas is in Venezuela, not Panama. Also, when the picture is shown to the audience, there is no indication of the ship's registry (no visible flag, crest, or wording). Ed would have no way of knowing that the ship was from Caracas.
In the opening scene, just as the Ayatollah starts speaking Frank Drebin (in disguise) is standing side by side with the Ayatollah's chair. Immediately following the next edit he is suddenly standing facing the chair.
In the video/theatrical release, in the final battle with Vincent Ludwig, Frank Drebin's chest protector has deflated without reason. (note: the network television broadcast adds a scene in which Ludwig shoots the chest protector, causing it to deflate.)
During the baseball scrum, Seattle #41 in gray swings a chair at LA #5 (Beverly), just as the chair hits him, the camera cuts to a tighter angle showing the chair breaking apart across #50's (Lombardo's) back.
When Frank is at the press conference, he picks up an almost empty pitcher and we see a glass is sitting behind it, then he starts pouring water his water into his glass. When they cut back to the scene there is now a full pitcher of water where the empty on was sitting.
As Frank gets up to speak during the press conference, the mayor sits with her chin resting on her hand. When Frank comments on how a queen might seem strange to Americans, it cuts to a close-up of the mayor and both her hands are resting on the table.
Ludwig mentions that the fish in his tank are 'Japanese Fighting Fish'. They are actually Lionfish. There are no actual 'Japanese Fighting Fish'. Siamese Fighting Fish, or bettas, are much smaller and cost much less than Ludwig says.
When Drebin is singing the national anthem, the American flag behind him is in the wrong position. The Union Jack is to the flag's right. US Flag protocol mandates that no flag should be on the American Flag's right (the viewer's left) when flown at the same height.
When Frank hits the trash cans in front of the police station, the airbags deploy and the second "airbag" pushes the gear selector up, causing the car to roll down the hill. In a car with an automatic transmission, the selector must be moved down to take the car out of 'park'.
When Frank Drebin is umpiring the baseball game, a scene shows four Angels players crossing second base during the same play. This is a joke, as the situation is impossible in baseball; even during a grand slam, only three players touch second base. The scoreboard later shows no more than 2 runs scoring in any inning, in keeping with the joke.