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.
Other mistake: In the newscast at the beginning of the episode, they incorrectly broadcast Robert Queen's birth date as 1948. They use the correct date in Episode 2 when it is shown as 1958 on his gravestone. (00:02:25)
Visible crew/equipment: When Oliver jumps out of the window of Adam Hunt's office, you can see the safety rope at the bottom.
Continuity mistake: When Oliver drinks his tequila, the hand with which he holds the glass keeps changing.
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.
Other mistake: When Oliver returns from the docks, he puts his bow in the case and his hood down. This is footage which is run backwards from the scene where he suits up earlier on. The best point to see this is when he ultimately blinks: it's very unnatural.
Continuity mistake: Yao Fei takes the bow away from Oliver in one shot, then Oliver hands it to him in a following scene. (00:02:10)
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".
Other mistake: Before the security guard is killed, he turns around and faces the direction of the camera. He is killed, and the camera backs up to reveal 6 men standing there. The security guard would have seen the men and he had time to react to them, but did nothing. (00:32:50)
Continuity mistake: When Oliver shoots Ted with an arrow, Ted falls down on the ground. The position of the arrow keeps changing from being perfectly in the center of the chest, to a few inches off-center, depending on the angle.
The Odyssey - S1-E14
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.
The Odyssey - S1-E14
Continuity mistake: When Wilson jams the pistol in Oliver's face, Wilson is holding the gun in his right hand. When the shot changes, it flips - he is suddenly holding it in his left hand, and his previous un-scarred left eye now has some scrapes around it.
Continuity mistake: When Oliver manages to wreck the Dodger's car, he skids his bike sideways and gets off. In the next shot, when the bike is in the background, he is no longer beside it, only to reappear in the next shot.
Continuity mistake: When Oliver takes the circuit board out of the missile launcher, Wilson grabs the radio to get out of there. But when he says "Leverage", the radio is back where it stood.
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.
Continuity mistake: When Oliver stabs the assassin with the poker, he pushes the thing all the way through, with the handle against the shoulder. In the next shot, there is a 3 inch piece of poker between the shoulder and the handle. (00:35:05)
Continuity mistake: In the flashback to when Oliver brings a pizza in and puts it on the bed, the box goes from open in one shot to closed in the next. (00:28:30)
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.
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.