Ray Palmer says "(Alpha particles) were unheard of in the 1970s." That is incorrect because Alpha particles were discovered in the 1890s. That's why Dr. Martin Stein corrects him "I will have you know that
I was researching Alpha particles when you were eating crayons!:" Thus they go to 25 year old Dr. Martin Stein to get the device to track Alpha Particles.
At 20:46- the phonograph which is playing the LP record "Ted Nugent" by Ted Nugent has the tonearm in the end groove where no music is recorded.
When Professor Stein, Sara and Jefferson arrive in Ivy Town in 1975, the students were dancing to "Disco Inferno" by The Trammps. That song was released in 1976.
At 09:20- Jackson is told to take the 1 megaton warhead to a "safe distance" which, on a plains, would be a BLAST RADIUS of approximately 4 miles. And he is told to "absorb" the blast which he clearly doesn't do. The bomb explodes and, after a few seconds, he REABSORBS the energy.
Carter and Kendra have been killed by Savage 406 times yet they still haven't worked on their strategy.
When Vandal Savage meets Hawkgirl and Hawkman in the mansion he adresses Hawkgirl in a modern slang of Arabic language not in an ancient Egyptian language.