In season 1 Cromartie's exposed metal skull travels through time with the Connors, but when John and Weaver travels through time together Cameron's damaged body is left behind.
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 yet, although the leading political party is seeking independence. Catherine Weaver would be correctly described as a citizen of the United Kingdom of Great Britain and Northern Ireland.
John Henry says he throws 20 when confronting the Mind Flayer, but on screen a 1 is visible. 20 is opposite to 1, so 1 cannot be seen on screen.
John Henry taking Cameron's chip was pointless as its her AI on it so at best she would be in the John Henry body.