The contents of principal Turchik's desk drawer changes as Danny and his reefer buddy search for Danny's radio. In the brief instant the drawer closes, several new items can be seen that were not there when the boys were ransacking the drawer moments earlier, including a set of Groucho Marx glasses, a toy ray gun, a yo-yo, a garden hose nozzle and a Playboy magazine. Gone from the drawer are a gyroscope, Pez dispenser in the shape of a pumpkin, and a set of finger cuffs.
While sitting on the couch drinking tea with Mrs. Samsky, Larry's hand can be seen holding the glass at various positions (higher and lower) as the scenes change.
When Traitle Groshkover - the Dybbuk - leaves the house in the opening scene, the snow is falling, and the ground is white. However, he leaves no footprints in the alleged snow as he walks through it.
The position of the Rabbi Nachter's tea bag string changes between shots, from the Rabbi's right hand side to his left and back again.
When Larry is telling Rabbi Nachtner about the accident, the tea bag is on the saucer and changes back into the cup between shots.
(at around 1h 10 mins) Larry is standing in front of the blackboard. The equation behind his right shoulder, "hbar = h/2pi = 6.6 x 10^-34 in [mks] units" is wrong. hbar = 1.05 x 10^-34 Js in mks units.
Yarmulkas (skull caps) are not worn in Hebrew class by students some of the time and then they are other times. The lettering on the school bus is in Hebrew which implies the school is not a reform movement school. They would always wear yarmulkas in class.
Rabbis are not wearing yarmulkas (skull caps) while at work in their synagogue.
Danny is called up as Maftir, the last reader for that weekly Torah portion. However, what he actually reads is the beginning of Parashat Behar, which is read by the first reader, not the last. The first reader would typically be a "cohen", a descendant of Aaron, the High Priest and brother of Moses. In light of their family name, it is reasonable to assume that the Coen brothers are themselves "cohanim".
On a close-up of a spinning record playing the track "Today" from the Surrealistic Pillow album, the label is A&M but the Airplane recorded for RCA.
In the final scenes where Larry changes Clive's failing grade, you can clearly see the erasure marks of the new grade before he erases the old one. This could denote the film makers needing several takes to get the right shot. Yet, it could also have been chosen to be included on purpose to show that Larry struggled many times with the morality of passing Clive, going so far as to update his grade, but had changed his mind.
Danny's transistor radio behaves like a 1980s Walkman. When it is confiscated it has rewound to (or been paused at) the beginning of the song. Marshak mysteriously knows what Danny was listening to when the device was stopped.
A Columbia Record Club representative informs Larry Gopnik that he received a copy of the Santana album "Abraxas". That album was released in 1970, three years after the movie was set.
One of the albums sent by the Columbia Record Club was "Cosmo's Factory", a CCR album released in 1970, not 1967.
Toward the end of the movie the Hebrew School teacher announces that "The Weather Service has issued a Tornado Warning". The National Weather Service was known as the Weather Bureau until late in 1970.
The school buses are painted yellow-and-black. During that time and into the 1970's Minnesota was one of two states (Nebraska was the other) that used orange and black for all school buses. It was only much later that they joined the more universal yellow-and-black color scheme.
In Minnesota, deer hunting season with rifles occurs in the autumn, while "tornado season" occurs from late spring to late summer. Two different dates in the film imply that the time of the year is in April and May, and the trees in the film have not changed color as they start to do in late August/early September. However, Larry Gopnik's neighbors return from deer hunting, well before the tornado scene at the end of the film.
Larry Gopnik teaches at a suburban college, but all of the mail he receives in his office is addressed to the zip code 55401. This zip code is in downtown Minneapolis, not the suburbs.
Larry Gopnik is writing an equation on the board in class. At one point he writes delta p equals the square root of ^2 - ^2 which would be zero, but the correct equation has the squared inside the bracket in the first term under the square root: ^2-^2. This is an equation for the root mean square deviation of momentum in Heisenberg's uncertainty principle of quantum mechanics. Later in the scene, after the students leave and Sy Ableman appears, the equation is in the correct form.
The mezuzah (a Scriptural passage usually enclosed in a small container, attached to the door of a Jewish home) affixed to the doorpost of the Sansky house, Larry Gopnik's neighbor, is on the left side of the entrance and tilted towards the outside. Mezuzahs are traditionally affixed to the right side of the entrance and tilt towards the house.
Larry's first name is spelled differently throughout the course of the movie. The sign on his office door reads "Prof. Lawrence Gopnik", but the letter from Meshbesher is addressed to "Laurence Gopnik" .
Larry tells the feds that they are sitting shiva over Sy Ableman. "Sitting Shiva" is done only by the seven relatives which are: father, mother, brother, sister, spouse, son or daughter. And since they are not one of the seven relatives they aren't supposed to be sitting shiva.
Rabbi Marshak tells Danny "When the truth is found to be lies, and all the hope within you dies." The lyric in "Somebody to Love" is actually "...all the joy within you dies".