After Molly selects her songs on the jukebox, a 45 rpm disc with a light yellow label is brought up to the stylus, but after the song has begun, a closeup of the jukebox shows a dark red Columbia label on the disc that's playing.
Mark Felt calls Howard to suggest he read a Bob Woodward and Carl Bernstein article about the Watergate break-in. Felt is looking at a copy of The Washington Post dated June 17, 1972 (which was the date the "plumbers" were caught). Bernstein was not assigned to the story until the next day, when he covered the arraignment in local court. Woodward teamed up with Bernstein even later. Thus, there's no way there could be an article by Woodward and Bernstein in the issue of the paper Felt is looking at. Indeed, the bylines on all the visible articles are by other reporters.
A copy of the Washington Post is shown with a date of "Wednesday June 17, 1972." In 1972, June 17th was a Saturday.
The movie is set in 1972, yet a Volkswagen Vanagon is shown several times on screen which was not built until 1979.
Agent Lambert uses a Maglite torch to search the taxi but Maglites weren't made until 1979 and movie is set in 1972.
When Harry hands his driver's license to the police officer, the license is still in his wallet. A police officer would require him to remove the license from the wallet before accepting it.
Although the movie theater marquee shows When a Stranger Calls (1979) and A Little Romance (1979), both of which were released in 1979, this is not anachronistic because the scenes where Harry is telling the story to Molly are set in 1980.
When Tommy is looking through the folder of baseball cards on the front porch, there is clearly a Roger Clemens 1988 Topps All-Star card. The film is set in 1972.
When Forest Whitaker is standing on the street following the robbery, an AMC Pacer station wagon can be seen passing behind him on the street. The AMC Pacer did not exist until 1975 and the wagon did not exist until 1977, five years after the robbery.