The transport plane that the car is loaded into on the ground is a C-123 Provider, which made its first flight in October, 1949. The particular variant depicted (with jet pods) did not appear until the 1960s. The air-to-air footage shows a different airplane, a DHC-4 Caribou, which first flew in 1958.
When Tucker is in his plant contemplating his impending demise, he drops his cigarette and puts it out, but in the next scene, he continues to press down his foot like there's a cigarette underneath it, but when he walks away nothing is there.
A wide shot is used showing the jury entering the courtroom with their verdict. The judge is shown standing as required for proper courtroom etiquette. Partway through the jury's entrance a cut is made to a slightly tighter shot but now the judge is dishonorably shown as seated.
During the nighttime scene between Tucker and Abe outside the Tucker plant, the red lit Tucker sign is on, then off, then on again before it is finally switched off along with all the other exterior lights.
The model car that the Tukerette uses at the unveiling to demonstrate how the engine can be removed for repairs has a front engine and different styling than the actual Tucker car. It is possible of course that this model is historically accurate for what may have been used at the actual unveiling of the Tucker.