After Ray restores main power to the Waverider, Martin explains to Gideon that Sara is dead. Gideon says "Luckily her brain cells are still functioning". Gideon then scans Sara to determine how she can help. Gideon could not have known Sara's brain cells were still active before taking the scan.
Neither officers nor enlisted soldiers of the British Army of the 1700s were permitted to have beards.
No soldier of the Revolution or even today would wear a hat indoors.
After Amaya rescues Nate from the river, Nate was feeling cold and Amaya warms him up with her body heat by skin to skin touch. But Nate does not remove him own wet cloths that would also be as cold as the water and major part of Amaya's body heat coming to Nate would be wasted on warming the cold clothing. Further, Amaya clothing would touch Nate's wet clothes so Amaya clothing would also become wet.
Nathanial was in the wave rider since 2016. He would not know what happens in 2017 when he was asked how people date in 2017.
At 01:45 -when Rip "shoots" General Washington the automatic pistol he uses does not eject a spent shell casing.
Amaya could have changed into a large, hairy mammal in order to better warm Nate. But then there would have been no "skin to skin" contact :(