The Library - S1-E3
Revealing mistake: In the extra 'Library' scene, the book that Bean is given already has the loose pages before he has been at them with the knife. (At one point the pages get pushed forward a little bit, meaning that they're not fastened into the book.)
Star-Crossed - June 15, 1972 - S1-E3
Revealing mistake: Sam stares at himself in the mirror and takes out his wallet to determine who he's leaped into. But the "reflection" in the mirror lowers the wallet and looks back up before Sam does. (00:05:20)
Revealing mistake: When the first fight starts, the Bloober disappears into thin air. (00:04:52)
Save the Max - S2-E3
Revealing mistake: When they are reading the reviews in the newspaper, look at the back page. It's the sports section. Next when Jessie comes back to Zack and tells him what Mr Belding was hiding, she says the paper is from 1968. But look at the back of that paper also. They are using the exact same paper. The reviews and the 1968 paper are the exact same.
Revealing mistake: When Arran is pushing his gran at high speed in her wheelchair through the care home corridors, it is obvious that his gran is a dummy.