Isn't the whole show unrealistic anyway? I think the part on rescuing the son is probably one of the more realistic one. I am not talking about the execution, but the motive. They are on the run, but they also know that whoever framed Lincoln will go after his son. Also Lincoln cannot just head to Mexico and live happily ever after knowing that his son will spend the rest of his life in prison because of him.
I agree that the re-attaching hand part was totally ridiculous! And why don't they wear disguises? I mean a pair of sunglasses and hat will help a lot. If you don't wear disguise, stay in the car and cover your face! Lincoln just stand outside of the store unshaven looking like a criminal. Even if I never read the paper or news and see him like that, I could think he is robbing the store.