The ribbons Hawkgirl are wearing are completely wrong. Ribbons go 3 across at the bottom, then 1 or 2 at the top, hers are worn as two rows of 3 and a third of 2 instead of one row 2 and rows of 3. Also the order is way off, the Navy and Marine Corps Medal and Purple Heart are shown at the bottom instead of the top. In other words, her ribbons are backwards and upside down.
Palmer says to Snart, "Be helpful to others. It's the scout motto." That is incorrect. In Boy Scouts, the Scout Motto is "Be Prepared."
Ray Palmer says, "In point of fact, I completed all 21 merit badges, including Nuclear Science, so I'm an Eagle Scout." However, Nuclear Science isn't one of the 21 required merit badges for an Eagle Scout. Additionally, it wasn't introduced until 2005, and for Ray to have been 18 or under in 2005, he would've been 15 or younger when he was in Professor Stein's class in college, which is not impossible but is unlikely, given that Stein claims not to remember him and someone of that age in an advanced physics class would presumably have been at least somewhat uncommon and therefore memorable.
A gun cocking sound is heard whenever a firearm is seen, such as when Valentina points the silenced handgun at Snart and when the guards point the AK-47 rifles. In her case, the gun she is holding has not been cocked. This sound effect is a common error in TV shows by people that have no idea how firearms function.
In the intro as hawk girls logo goes past it flashes back to rays face for less than a second.
Firestorm can survive a nuclear explosion but can't handle shorting out an electrical panel.
Pentagon security personnel leave their posts in order to investigate the sounds of an arm wrestling match.
In the Pentagon scenes, a number of military personnel are wearing their covers indoors. This is against protocol and they would have been required to remove them when going inside (with a few exceptions).