When the General is first stolen, Johnnie is washing his hands; when he sees the train pulling away, he walks away from the sink with his hands covered in soap, but in the following reverse shot where he tells the passengers what has happened, his hands are clean.
When Keaton is chasing the General in the Texas, during most of the chase the engine has a sliding hatch in the cab roof, but just before Keaton abandons the Texas, the roof changes to a smooth roof without a hatch, and slightly different shape, obviously meaning he changed engines.
The General and Texas are seen numbered 3 and 5, respectively. At the time the film is set, the engines of the Western and Atlantic were only known by their names, as were the General and the Texas. The railroads in the Confederacy did not begin numbering their engines until after the war. At that time, the General and Texas were numbered 39 and 49, respectively. The General did not receive the number 3 until the 1880s, and the Texas was renumbered 12 in 1880, then 212 in 1890, and never received the number 5.
When Johnnie gets switched on the siding, and reverses back onto the mainline, his locomotive slides a fair distance after the drivers stop, indicating that the rails have been heavily greased to prepare for the wheel slip scene following it.