Alana leaves the campaign office with her handbag, arrives at the restaurant with it, and takes it when she leaves with Matthew. When she leaves Matthew at his house, though, she no longer has it.
When Gary drops off Greg at the house, audio of a Dodger game is heard. Vin Scully is talking about Steve Garvey and the playoffs which would have been October 1974 not 1973 when movie is taking place.
The tune of the blessing over the Shabbat candles that Alana and her family sing is actually the tune for lighting Hanukkah candles. Furthermore, the blessing over the candles is seldom made at the dinner table, as candles can't be lit after sundown.
Early on, you hear video of Vin Scully broadcasting a Dodger game, and mentioning batters Steve Garvey and Jimmy Wynn. Wynn didn't play for the Dodgers until 1974. He was still an Astro in 1973.
When Jack Holden (Sean Penn) is riding the motorcycle on the golf course, the bike is heard to be shifting, but his left hand, on the clutch lever, never moves.
Alana listens to "Stumblin' In" through headphones while on a flight. The song was released in late 1978, five years after the date in which the film is set.
The type of crash or panic bars seen on the doors in the school gymnasium at the beginning of the film were not yet in use in 1973. The older type was typically a horizontal pipe lever.
When Gary and Alana are leaving the police station, there are solar panels on a building to their right. While "Solar One", one of the first solar buildings, was constructed in 1973, widespread proliferation of rooftop solar panels did not begin until the 1990s.
The blue Los Angeles city street signs are the more modern ones, not the older style that would have been up in the 1970s.
When Gary and Alana are parking the truck outside the home of Jon Peters, a red-light camera can be seen mounted atop a telephone wire. These cameras would not be used in LA until many years later.
In the long shot of running through the line of cars at the gas station (above the L.A. River), the LAPD motorcycle officers who are holding back traffic for the film crew can be briefly seen way down Victory Boulevard east of Lindley Avenue (about a block or so beyond the green traffic light).
Gary reveals to Alana that he has never before met anyone who is left-handed, yet when he introduces her to his casting agent friend Mary Grady, she is taking notes left-handed.
Gary is mistakenly arrested for murder. One of the arresting officers says to Gary "Have fun in Attica, dickhead" while he's in the back of the police car. Attica is in New York and he's arrested in California. This is a reference to Goodfellas. (The line in Goodfellas is "Bye bye, dickhead. See you in Attica, dick.") But Goodfellas was released many years after the time frame of the movie, so the officer couldn't be referencing it.
Alana asks Lance if he's circumcised and when he responds that he is she insists that means he's Jewish. Circumcision had stopped being a primarily Jewish practice by the early 20th century in the US. In Lance and Alana's generation about three quarters of American males would have been circumcised, while only about 3% would have been Jewish.