In the first scene, when Shane looks across to the Manhattan skyline, the MetLife building is visible, with "MetLife" in lights across the top of it. In the 1970s, this building was the Pan Am building with "Pan Am" in lights across the top.
When the IRS shows up to raid 54, the wide shot shows two unmarked police cars with red lights flashing on the dash. Then a tight shot shows an agent climbing out of a car and the light on the dash is blue.
Obviously, in editing, someone erroneously placed the New Year's Eve invitation close-up just before the Christmas party. Some considerable time later, there was a totally separate New Year's Eve Party and that NY Eve invitation close-up was undoubtedly filmed to appear just before it, not Christmas.
When Shane and Julie are bowling, Shane knocks down 8 pins including the 7. He then tells Julie he is going to to get the "7/10 split". When the camera shows the lane again the 7 pin is once again standing.
When Shane is bringing Christmas presents to his father's on Christmas Day, the radio station in his car is giving the stock market report for the day. The Stock Exchange is closed on Christmas Day. There would be no market update.
Many of the newspaper articles that are shown quickly are not the actual articles that match the headlines. The New Yorker article about Rubbell's arrest begins accurately, but the main body is an advice column. Two articles have identical copy. Some articles have blatant writing errors, such as misspelled words, missing hyphens, uncapped letters, etc. One article calls the Drug Enforcement Administration the "Drug Enforcement Administrative."