In season 1, Cromartie's exposed metal skull travels through time with the Connors, but when John and Weaver travel through time together, Cameron's damaged body is left behind.
John Henry says he rolls a 20 when confronting the Mind Flayer, but on screen a 1 is visible. 20 is directly opposite to 1 on that die, so 1 should not be visible.
Cameron can be heard cocking her shotgun when someone knocks on the door of a hideout that her and John are staying at. She cocks it again a few minutes later.
In season 1, it's established that Cameron has the same blue light in her eyes and blue visual interface as the female terminator in Terminator 3: Rise of the Machines (2003), but when her eye is shot off, the mechanical lens is red.
Agent Auldridge refers to Catherine Weaver as a citizen of Scotland. Scotland is not an independent country. Weaver would be correctly described as a citizen of the United Kingdom.
John Henry taking Cameron's chip was pointless, as it's her AI that's on it - so at best, she would be in the John Henry body.