Character mistake: When Oliver is brought into Fires' tent, he gets pushed into a pole by one of the guards. Take a close look at his handcuffs. They are so loose, he could easily escape from that. Not only that, but no guard who had any training would ever put handcuffs so loosely on someone they would treat as "hostile".
Factual error: There is no way Laurel Lance would have been allowed on the prosecution team for Moira Queen's murder trial. Due to the facts that she used to date the defendant's son, the defendant's daughter used to intern for her, and her boyfriend was one of the people killed in the Glades it would have taken all of two seconds for the court to have her removed if she didn't willingly recuse herself, since her presence would be a major conflict of interest.
Factual error: When Oliver is hunting Prometheus, they come face to face. Oliver fires an arrow, which is tracked in slow motion before being split by one of Prometheus' throwing stars. Problem is that Oliver's arrow is, well, flying straight as an arrow. But in reality, when you film an arrow in slow motion, they flex and wobble, and definitely wouldn't fly like the one shown on screen.
Character mistake: At one point Felicity says, "There's at least a teraflop of data to go through." Felicity is a computer genius, so she should know that a teraflop is a measurement of processing power, not data storage. She should have said "terabyte."
Factual error: Felicity apparently extracts DNA from the tooth of one of Damien Darhk's men. She then realises that the DNA lacks "half of the genetic markers" by looking at an optic microscope. Skipping the fact that this sentence makes absolutely no sense whatsoever, you certainly cannot analyse genetic markers by simply looking a tooth with an optic microscope.
Continuity mistake: In the scene in the garden where Oliver and his sister stand by the headstones, Robert Queen's birth date is carved into the stone as 1958. This conflicts with the news report at the beginning of episode 1 when his birth date is shown as 1948.
Factual error: Felicity tracks the abducted team members to latitude and longitude values that are negative, which she and others present regard as impossible results until they realise the captives are in outer space. In actuality, south latitudes are conventionally represented as negative, as are west longitudes; and negative values would not convey information about an outer space location, which would instead be referenced with celestial coordinates.
Visible crew/equipment: When Slade brings the drink in the forest (referring to Billy Wintergreen), you can see shadows of people walking upstairs in the background behind a big white curtain.
Deliberate mistake: During the big battle, Arrow is knocked down and when he opens his eyes, the reflection in his eyes is tilted over to give the sense he's seeing things sideways. But the reflection should still have shown the proper orientation no matter what orientation his eye was at. Think of looking into a mirror and then rotating the mirror to the side, the reflection wouldn't rotate.
Revealing mistake: When Oliver breaks into the building and draws his bow, there is a laser pointed at the tip of his arrow. He is told that if he moves a muscle and removes the tip of the arrow out of the of the laser that he will die. But shortly afterwards, just before Oliver looks over at the TV, you can see the arrow tip move out of the way of the laser and see the laser reach the other side of the wall for a split second.
Factual error: In this episode Barry uses rat poison to save Oliver, from a poison that coagulated blood. Though rat poison contains anticoagulants like Warfarin, this is medically wrong because, It takes at least 1-3 days for Warfarin to be effective and it may even cause excess of coagulation during this time. It could never have saved Oliver instantaneously. What Oliver needed was heparin. So Barry in real world instead of curing Oliver might just have made him much worse.