The position of Cat's arms varies between shots when we first see her, just before she says Sandy Bullock stole her bike at spin class.
Winn says that he analyzed Siobhan's typing speed and patterns "on the hard drive". While this is possible if her typing was suitably recorded, the dialogue makes it sound as if this can be simply done retroactively using the mail on her office computer as a template for the analysis. That is not possible.
The snake that drops from the tree in the Peruvian jungle, and that J'onn J'onzz picks up, is a Burmese python. It is native to southeast Asia, not South America.
At the beginning of the episode when they're showing the news 3 report, the scene is shot like it wasn't initially supposed to be a news report, and the camera angles of the news reporter, and Supergirl are not filmed like any news stations would film them. It is apparent that the reporter isn't even looking into the camera, but you can see where she is looking at, and where she's looking at there is a guys hand holding a camera, just further proving this scene wasn't initially supposed to be filmed as a news report.
The Army uniform worn by Lucy Lane uses the hat emblem of an enlisted soldier; the eagle emblem worn by an officer is not surrounded by a ring.
When Alex is talking to J'onn in his glass holding cell, you can see the a crew member who is wearing a hat, and glasses in the glass reflection.
Lucy Lane, supposedly a career Army officer with the JAG, is wearing her hat indoors, an act that is against military regulations for all US military personnel.
If Lucy Lane is JAG officer, her oath would require her to report to the highest officials that an American citizen (Alex) was being detained without due process of law.
Hensha, speaking to the other agents, issues the order "Shoot to kill." This is redundant, since any shot has the potential to kill, there is no order of "Shoot to wound."
When Lucy and the other officer are interrogating Alex about Hank. She asks her if she knew he was an alien, when she was recruited. She answers, and a flashback starts. After the flashback, Officer Harper asked Alex again the same question, as if it were the first time.