Deliberate mistake: Whenever Deathstroke is on screen, he has three grenades for a launcher strapped to his chest. But on closer inspection, you can see these grenades are actually BB-gun grenades: You can tell by the very distinctive holes at the tip. They did this because launched grenades are A) very expensive and B) not very safe to walk around with on set. A few of the most noticeable times are when Yao Fei is fighting him when he is freeing Oliver in episode 5 and when Oliver is talking to him in episode 14.
Continuity mistake: During the hallway gauntlet, Oliver takes a guy out and ends up on his left knee. He then starts to turn right and draws an arrow, which doesn't make any sense because he holds his bow with his left hand and can't get a good shot from that position. What's more, in the following shot, he is turning to his left.
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".
Revealing mistake: After Fires shoots Wilson, he shoots a few more times with the camera on him. Here you can see that the muzzle flash is pretty obviously CGI. Look for things like that fact that it's very small, there's no light shed on the car beside Fires or on himself and there is no smoke.
Audio problem: When Oliver is fighting the guys in the hallway, he shoots the second to last guy. But when he starts to draw an instant beforehand, you can see that his right hand, with which he holds the arrow, is nowhere near the quiver when the sound of the drawn arrow begins.
Factual error: When The Hood busts into the underground casino, the throws a guy through a glass table, and it breaks into large shards. He then proceeds to grab a handful of safety glass, so it's not the same glass anymore, and he throws it into the face of a guard, and it hurts him badly. Safety glass is designed precisely to prevent that. It is impossible for the pieces to get lodged in the guys face, no matter how hard The Hood throws them.
Other mistake: When the Huntress is attacking the safehouse, she fires a shotgun blast at Green Arrow who's several feet away, hitting a door behind him and leaving a small hole, as would be made by a slug, rather than pellets (which would have spread out a lot over that distance). She then shoots the door lock right next to her, which gets riddled with small pellet holes.