As Jake and Bill walk along Elm Street, Dallas the train behind them is moving at different speeds in different shots.
As Jake is attending to his duties as a teacher in Jody H.S. in 1962, several current students are seen both in the hallways and later at a school dance wearing letter jackets that are clearly marked class of "60.
When Bill and Jake are bugging Oswald's apartment, they are using LED flashlights. Jake didn't bring LED flashlight technology with him through the Rabbit Hole to 1960 and it wasn't made available to the public until 1999 by a company called Luxeon.
At 7:03, you will see James Franco's character and companion walking into Dealey Plaza where the Kennedy assassination takes place. To the left of the shot at exactly the time indicated, you will see two light brown patches on the sidewalk. This is where the street sign, seen in the Zapruder (2000) film, should be, however it is absent indicating they are walking through Dealey Plaza while clearly not in the 1960's.
When they change the tape and plug in their headphones, the stereo 1/4" jack shown is a Neutrik NP3C, Neutrik wasn't founded until 1975.
Signs at Dallas Love Field show Delta flight 835 departing at 19:45. In 1962, Delta 835 operated from Chicago to Miami via Memphis and Atlanta, not stopping at Dallas.
Before the opening credits when asked "You come from the future, when?" Franco says 2016 but his lips say 2015.
Jake and Bill get out of the car and talk briefly after arriving in Dallas. There is a nearby building in the shot with a large window that is reflecting contemporary street signs.
Although contemporary road signs and markers commemorating the JFK assassination have been digitally edited out of the scene where Bill and Jake walk along Elm Street through Dealey Plaza, the back side of the State of Texas historical marker commemorating Dallas pioneer John Neely Bryan can be clearly seen beyond the white wall at the top of the grassy knoll. Their visit predates the initiation of the Texas Historical Marker Program in 1962, much less the existence of this particular marker.
It is not possible for a school prom in 1962 to play Little Eva's Loco-Motion as it wasn't released until June of that year.
The Roberts 770X tape recorders Jake and Bill use to record the Oswalds were not introduced until 1966.
When Jake and Bill arrive in Dallas, there is a reflection in the storefront window that shows modern-day parking signs.
When talking to his class about the Poe tale A Cask of Amontillado, Jake refers to Fortunato building the wall to seal in his victim. In the story, Fortunato was the victim, being built into the wall by Montresor.