During Jake's and Brian's slow-motion walk down the busy street, there is a man wearing glasses and a cream-colored jacket. As they approach, the man repeatedly jumps in front of/behind them between shots.
When Jake and Brian are inside the karaoke shop talking with the salesman we can see that the outside world constantly changes from night to day through the windows and door.
In the cafe scene when they are discussing the upcoming "double-date," Anna's hairstyle changes from a ponytail to braids in one shot, then goes back to a ponytail for the rest of the scene.
Brian shows a picture to the bartender, clearly showing the kids' torsos. Then when Brian starts explaining who the kids in the picture are and we see the picture again, the kids are much closer to the camera and their torsos are no longer visible.
When Anna and Jake's mother sit on the sofa looking at pictures of the Schram's wedding, you can see that Anna's hair line is darker the rest of her hair - she obviously has to redye. In the next scene which plays maybe 1 hour later in the story, her hair is all over blonde.
The rabbi works with a young man on his Torah portion but refers to it as a haftarah. Also, the bar mitzvah boy is studying the first chapter of Genesis and has his bar mitzvah before the Jewish New Year. This portion is read after the Jewish New Year, not before.
Some of the scenes that supposedly take place on Yom Kippur are not realistic. Yom Kippur is a solemn day of fasting, prayer and repentance, and observant Jews spend basically the entire day in temple services. Following Jake's Yom Kippur "speech" as they called it (there are not "speeches," they are called sermons) the board of Jake's temple appears to have a meeting to discuss his career. This would/could never happen since no work is allowed on that day. After the meeting concludes, Jake finds out he still has a job and he and Anna go to the karaoke party. There is no way Jake, Rabbi Lewis and Jake's mother would be at a karaoke party on Yom Kippur.
During the conversation between Jake and Brian, after the fight in the synagogue, the camera is on Jake's face from behind Brian's shoulder at one point. You can clearly see that he is not talking, and yet we hear Brian's voice.
Reflected in a wall picture in the hallway when Jake is being reproved for his sermon antics.
Brian describes 13-year-old Anna as "a cross between Jonny Quest (1964) and Tatum O'Neal in Foxes (1980)". Tatum O'Neal wasn't in Foxes. He's either referring to Jodie Foster in Foxes, or Tatum O'Neal in Little Darlings (1980). Then again, he was drunk.