As Winn enters the arcade on the boardwalk, there is a child's mechanical ride just outside the door with just the Superman symbol on it. Afterwards (when Winn is being interviewed by the cop) the same ride now has the word "Superman" above the symbol.
When eating pizza with Alex, Kara's slice goes between bent and straight between shots.
At 28:20 into the episode J'onn J'onzz and Agent Danvers say the product of Sodium Sulfite, and Sodium Iodate is hydrochloric acid. Or in chemistry terms
NaSO3 + NaIO3 --> HCl since neither of the reactants contain Chlorine this suggested chemistry is impossible.
When his father escapes from prison, Winn is interviewed by the FBI, who are trying to apprehend his father. However, escaped fugitives, especially those that have escaped from federal prisons, fall under the jurisdiction of the United States Marshals' Service, not the FBI.
Supergirl (Melissa Benoist) possesses a host of super powers, including frequently-utilized X-ray vision (seen in this episode as well), yet is fooled by Toyman that there is a little girl held hostage in the wooden crate, which she has to open to find out it is only a doll.