At the end Lucy discovers that she was accidentally caught in a photograph taken at the event. However, the camera technology of that day was so crude that people had to stand still for a couple of minutes while the photograph was being taken. She could not have been taken by surprise by the photographer, especially since she is shown looking at the camera, and would have known what was happening and had time to get out of the way.
Jesse James fires the modern rifle in fully automatic mode for nearly 20 seconds. And while the rate of fire is unrealistically low, he still spends much more ammunition than the magazine can hold.
Emma Whitmore comes back to modern day, holding a beer then says "oh wow did I miss beer", except the era and place she was living for the last 10 years being a historic period, beer (hops free) would have been likely one of the few safe water sources and a huge portion of daily diet. The line could have had 'beer' be substituted by almost any modern packaged food or beverage other than beer/wine.
Jesse James is shown armed when the Ford brothers attempt to assassinate him, with no one else home. In reality, Jesse James was unarmed when shot by Bob Ford, and his wife came running from the kitchen after hearing the shots while his children were playing in another room.
Jiya tries to cover her actions by saying the software for the trainer is sluggish and needs decompiling. Decompiling is only necessary when the original source code is not available. As the engineers who built the system still have access and control of the hardware and software, this would be completely pointless.
When the camera pans out above showing the carnage that Jesse James did to the Indian scouts, heavy equipment tire tracks can be clearly be seen in the snow.