Other mistake: When Kevin and Perry go home to find the postman at the front door, the postman asks Kevin to sign for a letter (his father's). If you look closely at the address on the postman's sheet it does not match the address on the letter. You need to be quick and look closely.
Other mistake: After Jody, Charlie, and Cooper take their last curtain call, the shot goes backstage. Sergei yells at Eva, "You! I'm gonna kill you!" presumably because she surprised him by taking Maureen's place. Eva responds, "I'm so sorry. I wanted to tell you." And they argue playfully and then hug. But it's been a long time [the entire length of Cooper's ballet] since their ballet finished. And we saw the backstage scenes immediately after Cooper's ballet and after the Italian Symphony ballet, and everyone had a chance to talk right then. And Eva and Sergei finished their ballet in each other's arms. So they should have had that whole conversation a long time earlier. Even if real ballet dancers wouldn't be permitted to talk after a performance, the dancers in this movie are shown speaking freely to one another backstage as soon as the curtain falls. (01:44:05)
Other mistake: The radio station had no power or telephone lines anywhere in the vicinity, and the lines would not have been buried in 1937. A telephone is seen on the wall inside the building, yet it couldn't have been connected to anything. There wasn't a generator to power the radio transmitter, because it would have had an exhaust pipe through the roof, nor was there any adjacent building to house a generator.