Iris gets a perm, but for the next few scenes her hair is still straight.
The first time we see Iris' house, there is an air conditioner in the upper left window. The next time we see the house, the air conditioner has disappeared.
The final shot of that sequence supposedly takes place at Post and Washington Streets, but a street sign partly out of focus in the background is clearly different from either of those.
Iris's sister and brother-in-law just disappeared without any explanation. Since they were virtually broke, they would have been home all the time.
In the map-reading exercise, several of the street signs visibly have stickers pasted on them to change the (Toronto) street names.
When Stanley returns from Detroit, his car is shown to have a Michigan license plate on the front of the vehicle. Unlike many states that issue license plates for both the front and rear of the vehicle. Michigan issues plates for the rear of the vehicle only.
When Stanley is telling Iris about the disadvantages of being illiterate, he states that he cannot ride the bus because he can't read the street signs. But at the first of the movie when Iris's purse is grabbed by a purse snatcher, Stanley comes sprinting out of the back of the bus to give chase, indicating he has in fact been riding the bus. Also, street signs would be an issue no matter what his mode of transportation.
It is extremely to get even the most menial job without being able to sign one's name - also impossible to sign someone into a nursing home or cash a paycheck.
How Stanley baked all those cakes for his cake cooling machine is never explained.
The film completely skipped over how Stanley met, and who Stanley met, to launch his new career.
Certainly the first thing, and the most important thing that Iris should have taught Stanley was how to read and write his name.