Character mistake: After Anakin says to use the walkers (AT-TEs) as boarding vessels, Rex calls the first one an AT-AT (a vehicle that does not even exist at this point in-universe) while ordering a battalion of clones into it. (00:04:10)
Adios, Señor Magistrado - S1-E26
Character mistake: During the tavern meeting, Sergeant Garcia calls Magistrado Carlos Galindo "Comandante."
Character mistake: Bret fires at "John Wesley Hardin" four times, but the doctor and all the witnesses say there were three shots.
Character mistake: Troy calls for the "Twistornado" but his card reads "Windrive"; the cards have always read exactly what the rangers called for.
Character mistake: When the office receives a code red alert, there is a close-up shot of the alarm, where there are two clocks next to it. One of the clocks represents New York time. The other represents London time. The clock representing New York reads the time as 10:40 and the clock representing London reads the time as 4:40. The time difference between New York and London is 5 hours, not 6 (occasionally 4 due to DST). (00:03:40)
Suggested correction: London is five hours ahead of New York normally, but Episode 5 takes place on April 25, 1946, so it is reasonable to assume Episode 1 takes place not long before that. England went on British Summer Time on April 14, 1946, while New York didn't go on Daylight Savings Time until April 28, 1946, so from April 14 to April 28, 1946, London was 6 hours ahead of New York, so the clocks would be correct.
Proof Through the Night - S1-E4
Character mistake: Dominic said the MIGs were coming in 015° but the readout says 105°. If they were at heading from 015, the triangles representing them would be in the upper right quadrant of the radar circle, close to the zero.