Plot hole: Lee and Dawn overstay their tourist visa in the US, then fly back to the UK for the Office Christmas party. They then get into a taxi to go out to the airport in order to return to the US. They're kidding themselves. As I know (to my cost) when you overstay a tourist visa, the US Immigration Service finds out when you check in at the airport on departure. They'll be refused reentry, and probably barred from entering the US for up to six years. (I got a three year ban.) Neither Lee nor Dawn could possibly be unaware of this nor think they could beat the system as they would have been arrested when they checked in in Florida on departure (as I was), and they would have remained in small holding cells until the paperwork banning their return had been processed and their passports stamped 'Invalid for U.S. Entry', as mine was. (All this takes about seventy two hours, so they'd have missed the Christmas party anyway.) The mistake is NOT that they were able to leave the USA - that is explained (it's still not possible, but in the context of the show and the suspension of disbelief we are meant to believe it) the mistake is that they are on the way back to the airport to return. That's absurd. They would have been under no illusions as to their banned status re reentry to the USA.
Character mistake: Nicole Wallace has murdered and stolen the identity of Professor Elizabeth Hitchens, who was Australian. While speaking to Detective Goren she refers to her life in Melbourne, pronouncing it the American way : "Mel-born." No Australian would do such a thing - it is pronounced "Melbun." A detail-obsessed knowall like Goren would pick up on that immediately.
Factual error: In this episode we see Blithe get shot in the neck and are told that he died in 1948. In reality he was shot in the shoulder and survived. He later served in Korea and was promoted to master sergeant as well as receiving the paratrooper of the year award. Blithe died in 1967 while on active duty in Germany.
Continuity mistake: When Flash plays tag with Faust ("Now you see me, now you don't"), there is a brief shot in which he rushes at Faust - but not inside Hyppolita's palace, but in some high-tech laboratory. Obviously a shot from some earlier series, since the coloring and style are different from the Justice League's.
Plot hole: In the start of season 4 we meet Liberty's little brother, Danny. J.T. and Manny are making fun of him because he is new to the school and is starting out. If he is starting out, then he should be in the 7th grade, because it is stated in the first episode that the school changed into a 7-12. Liberty, J.T., Manny, Emma,Toby etc. are all in the 10th grade so how does it end up that Danny is a grade below Liberty?
Factual error: Aetius' troops don't look anything like 5th century Roman soldiers. They are carrying a large rectangular shield, a pilum (a spear which was used for throwing) and a sword (gladius) on their right. This was typical for the Roman army until about the 3rd century A.D. In Aetius' time, the soldiers would have had smaller oval shields, a hasta (a lance used for stabbing and for fending off cavalry attacks) and a sword (spatha) on their left. Also, there would be an enormous amount of "barbarian" mercenaries in the Roman army (Goths, Vandals, even Huns.), so it was hardly a Roman army anymore. And where's Aetius' cavalry?