Corrected entry: Early on, The Flash's immense speed caused his clothes, and those of people he was carrying, to catch fire because of the air resistance. Gave him an excuse for the suit, but this effect was fairly quickly forgotten, with him frequently carrying civilians or running out of costume with no ill effects at all.
Corrected entry: Barry gets 4 cups of 'Flash'. They are with four people (Barry, Caitlin, Cisco and Iris) but look at the next shot; everyone's drinking except for Caitlin, but the fourth cup is still going up in shot, meaning a random extra person has appeared. (00:05:26)
Correction: It's true Caitlin is not drinking her cup but you see Cisco holding 2 cups of coffee.
Continuity mistake: When Joe and Iris are going to talk to Matthew Kim, Iris is already wearing the suit that Cisco later makes for her, she just wears it open the first time and closed the second time. (00:13:41 - 00:29:50)
Suggested correction: She is wearing the jacket when speaking with Matthew Kim because it is her jacket. When Cisco has her new outfit in the suit bag, he said something to the effect of "I had to make do," meaning that it was short notice and he could not make her a suit like he did for other speedsters. She is essentially wearing regular clothes with a mask, and her jacket was part of that outfit. Quite frankly, all the clothes could have been hers, but we know the jacket is.
Not only that, but in the scene before, we see the jacket hanging over her chair. So just something she wore that day.
Corrected entry: After being broken out of prison by Mark Mardon, the Trickster sings, "Deck the halls with body parts from a girl named Harley." This is a reference to his roles as the Joker in "Batman". (00:09:50)
Correction: He doesn't say "Harley", he says "Holly". It has nothing to do with his role as the Joker, but just changing the lyrics which normally go "Deck the halls with boughs of holly."
Crisis on Earth-X, Part 3 - S4-E8
Corrected entry: Turns out Oliver was handed an unloaded weapon by evil Quentin. But Oliver's handled enough weapons in his time to know that a gun with no bullets is noticeably lighter than one with, and would have realised the ruse immediately, certainly not then trying to threaten Quentin-X with it.
Correction: It was an unfamiliar weapon from another universe. He wouldn't know its mass.
Fast Enough - S1-E23
Corrected entry: At one point near the end of the episode, Professor Stein says to Barry, "That event has an energy level of at least 6.7 teraelectron volts. It cannot be stopped." One TeV is a measurement used in particle physics and is a very small amount of energy, approximately that of a very small flying insect. Hardly a proper measurement for a huge, catastrophic event.
Correction: Teraelectron volts measure particle energies, or their acceleration. The power comes from the amount of space the energy is squeezed into. The Large Hadron Collider accelerated protons to 1.18 teraelectron volts, so not much more than a mosquito, but a trillion times smaller than a mosquito, so quite powerful. The energy reading from Stein is over 5.6 times more than the world's most powerful superconducting proton synchrotron, and it's crammed into a very small space, making it nearly unstoppable.
Going Rogue - S1-E4
Deliberate mistake: When Capt. Cold is about to shoot Joe in the train station, Eddy "shoots" a pillar next to him to make him run. Eddy then comes from behind the pillar that got shot with no cuts. He would have had to been on the complete opposite side to shoot the pillar where it was hit. (00:32:50)
Suggested correction: I watched the scene several times and nothing indicates the pillar was shot from the left side. It looks like the pillar was shot from behind (which is why there's no hole on the side or front), exactly where Eddie would have been standing.
Correction: This is half-true. Barry's connection to the Speed Force allows for some sort of shield around his body that protects him from harm while running. In the beginning, his bond with the Speed Force is weak, whereas later on, he becomes closer and closer to the Speed Force, allowing him to run faster, defy laws of physics, etc.