Artistic License - Medicine: When the modern task force is sent back to 1942, several crew members have seizures, and Col. Lonesome Jones is seen clearing the airway of a man who's swallowed his tongue. In real life, both neurologists and epileptics know that you can't swallow your tongue in a seizure. In fact, sticking your hands or an object in someone's mouth to protect their tongue is liable to cause more damage.
I could never figure out why the uptimers didn't just drive to Berlin and sail into Tokyo. They showed the ability to attack the Axis forces with pretty much impunity. I understand why they went after the POW camps, they felt really sorry for the POWs, but they could have gotten the same effort and ended the war three years earlier, by nuking Tokyo and landing the 82nd MEU in Germany and driving them to Berlin.