"On July 16th, 1945, in the mountains outside of Los Alamos, New Mexico, the world's first atomic bomb exploded." Trinity Site is actually some 200 miles south of Los Alamos.
In the cell phone store, after Andy explains all the bells and whistles of the new cell phone, Sarah asks if she can make a phone call by pressing the numbers 1 through 9. She should have said 0 through 9 as 0 is a common digit in telephone numbers.
The 'blood' covering the floor and walls of the scientists home is still red, though when blood de-oxygenates (through natural metabolism) it turns dark red then brown until it dries, shrinking and taking on a crackly appearance. Only blood fresh from the body is bright red.
When Cromartie forces the scientist to make the synthetic skin, we get a shot of the scientist in the bathroom with the robot who has an over coat on. In the next shot, we see the scientist becoming amazed at the sight of the robot without the coat. If you compare the gigantic size of the robot that they show next, with the figure that was in the overcoat, there is an obvious difference in size. The real Cromartie could never fit in that small of an overcoat.
While it is true that Moe Berg was sent by the OSS to determine if Werner Heisenberg was close to making the atomic bomb, the event occurred in 1944, not 1943 like Sarah said.
Agent Ellison refers to Enrique as Enrique Salzia. In James Cameron's Terminator 2: Judgment Day (1991), the character's last name is Salceda.
In the pilot, Cameron the Terminator is so advanced it even actively uses metaphors, like calling the time machine hidden in the bank vault 'hope'. In this episode, it can't even understand other people's metaphors like in 'it's not brain surgery'.
When Cameron the Terminator triggers the metal detector at school, John tells the security guard she had a metal plate in her head because of an accident in her past. The guard then swings a hand scanner at her head and lets her pass. An actual security guard would scan her whole body with the hand scanner in order to check if she was hiding a weapon, thereby discovering her whole metal skeleton.