A bit over 32 mins into part 2, Rufus tells Lucy that Wyatt tried to blowtorch his way out of the bunker to go find her. He actually used a grinder.
At the end of the first season Flynn gives Lucy her diary that she gave him. In this episode an older Lucy gives present day Lucy the diary again. Unless the diary changed because of the things that the gang changed older Lucy wouldn't need to give present day Lucy the diary again.
Even after Rufus is saved, Lucy still is shown with the bruises she got from her dust up with Emma in 1888 San Francisco. The problem with that is that since they saved Rufus, they never went there and they never fought, so she shouldn't have any cuts.
At 16:20 in part 2, the snow that was on the ground previously has totally disappeared.
Emma and the sleeper agent grapple over a bucket apparently full of gold nuggets. They handle it as though it's very light. It would likely weigh 100 pounds or more.
Emma handed Jessica two gold bars with one hand. Gold bars weigh 400 troy ounces, which is approximately 27.43 lbs each. Handing over nearly 55 lbs with one hand as easily as she did is impossible based on her visible size.
Mason says that the Soviets first had an atomic bomb six months after the US Japan bombings in August 1945. The Soviets didn't detonate their first atomic bomb until four years later in August 1949.
As the team walk into town around 2:45 into part 2, the ground is covered in snow but there is none on the trees, buildings or vehicles. The blue coloring of the picture tries to hide the blazing sunshine.
After being stopped by Joaquin Murrieta, Wyatt mounts his horse from the right side rather than the left.
The second part of the episode is set in a frozen winter, but the length of the shadows suggest that the sun is nearly overhead. The odd coloring of these scenes suggest that a blue filter was used to disguise the fact that they were (probably) filmed during summer in strong sunlight. This is first noticeable at 40:50 into the first part of the story.
At 15:10 into part 2, an extra on a walking stick can be seen signaling straight at the camera. Even leading actors don't look directly at the camera unless giving the viewer dialogue.