That's where semi-automated variable margin of error using previous frames to determine speed of players would come into play. Given what I've seen of the automated system they could easily do it as it tracks their position every 0.02 seconds. They can see in the frames around the frame of the ball being played if players are standing still, slightly moving, jogging or running full pelt.
From that they can get the crossing speed of the 2 players (even if going the same direction) and a simple calculation gives them a possible distance covered between frames. It's not rocket science as it's simple to implement as it's basic mathematics to work out. The margin of error increases with speed along the lines of braking distance when travelling at speed as it's the same thing. If they try to be precise again like they did when it first came in without any benefit of doubt for the attacker then it's a big mistake.
My thinking is that using that method means a player standing goal side of a marker on a free kick for example would always be offside as his previous position and speed compared to the defender wouldn't allow a big enough margin to cover his body width. It's physically impossible for someone to suddenly move around the side and in front of another player in 0.02 seconds.
As for mistakes, they could eliminate incorrectly called onside decisions by allowing all the margin of error in favour of the attacker. The only debatable decisions would be close onsides being given that could possibly have been offside. No method can ever be perfect and the linesman only method, although it's never going back to that, means it could go either way and far bigger an error than a toenail on occasion.
Even the semi-automated VAR isn't perfect if it's trying to determine the exact position without any error margin. It would have picked up on the offside Lee Mason missed as mentioned above and be a lot quicker as it wouldn't need reviewing in such detail like he did with the 1st offside.
I replied to the daylight thing earlier but it had me thinking as to how it would work. I don't think they can have a daylight rule as that means attackers could partially block defenders while having no daylight (they couldn't just stand fully in front of them as has already been picked up earlier in thread). Even if they did bring it in they would still need an offside line creating so they'd still have the error of margin to debate. Given the advantage of daylight then it could be giving a further advantage to the attacker with him being well offside yet being given onside. This is a basic example of the daylight rule using the current rule in the 1st image. You could have a player's trailing toe playing him onside against another player. The 2nd image is the using the torso as the line instead of body parts, still just offside here.
Even as it is now, you'd have people pointing out that one player is leaning forwards and one backwards and where exactly do you look for daylight, the arse end or the nipple end of the torso? Plus if you factor in the margin of error and give it to the attacker to remove doubt then in reality there could be even more daylight between them given the margin of error is the probably already the thickness of a torso front to back.
VAR and the offside isn't going away so they need to make it as good and fair as possible. It will the automated system sorting offsides a lot quicker probably next season. For me, this system using the level rule plus the variable error margin depending on speed of players in favour of the attacker would be the lesser of all evils. That's because all the goals would only only be ruled out for 100% offsides. Watch us have a dogdy offside or decision against us today, though him in the blue looks rapid for a forward and I think he's a free agent so ger'im signed!