At the very beginning of the movie, Mitch gets up at 5:16am, goes jogging with his "cow", then commutes by train from his home in New Rochelle to downtown Manhattan and arrives to work at 6:07am (see clock in background over his head). Can't be done.
When Mitch is walking to work on his 40th birthday, he passes by the Ed Sullivan Theater, which prominently displays a sign for the Late Show with David Letterman. Since Mitch was born on September 8, 1952, that would make the date September 8, 1992. The Late Show didn't premiere until August 30, 1993.
After duke saves Mitch, Phil and Glen from the two cowboys they rented the equipment from duke cuts the ropes on their hands and Mitch says "Curly were so sorry we thought you were dead". However his mouth does not move.
In the shot of the train arriving at New Rochelle, the train pulls past the green 'New Rochelle' marker sign. However the train is heading in the opposite way of the writing on the sign, indicating that the train is in fact leaving New Rochelle, not arriving as implied.
When Mitch (Billy Crystal) and Barbara (Patricia Wettig) are in the other room arguing about Glen (Jon Lovitz) while he's reciting dialogue from "The Godfather Part II" to Phil (Daniel Stern), if you listen closely, he says "This is the business we have chosen! I didn't ask who gave the order!" followed by "Someone put a bullet in his eye!" In the actual Godfather film, the lines are reversed. Speaking about Moe Greene, Hyman Roth says "Someone put a bullet in his eye!" first, then "This is the business..." afterward.
After the night of nearly freezing and Dukes fake death, he points to the "frozen people" and Mitch looks through the telescope looking down at them. When the camera angle changes,to appear to be looking through the telescope, the angle is now looking UP at the frozen people.
When the map is on fire, the wind blows it around whilst the guys chase after it to put it out. However whilst they're running after it, the leaves on the trees and the bushes they run past don't move at all, proving that there is no actual wind.