Obviously there's also the second part of this clause that is required for it to be offside - "when this action impacts on an opponent" (interestingly, not "impacts on the ability of an opponent to play the ball" in this case). .
Except that, as I mentioned earlier, the IFAB memo that introduced this clause goes on to explain that the impact being talked about does indeed refer to the impact on the opponent's ability to play the ball. But seeing as they had spelt it out in full in the clause about an obvious action, I suspect they just didn't want to be repeating the same phrase over and over. .
First of all let me commend highly the standard of debate in this thread. So nice to see thoughtful and intelligent discussion that does not descend into cheap insults and backbiting. Give yourself a pat on the back guys!
For my own part, I tend to side with those who say deliberate handling, but this is a real judgement call.
On the offside question, there is a subtle point about the difference between the following parts of the Law: Interfering with an opponent can mean blocking line of vision, or challenging for the ball. It also means (my numbers added for clarity):
1 - clearly attempting to play a ball which is close to him when this action impacts on an opponent
or
2 - making an obvious action which clearly impacts on the ability of an opponent to play the ball
GraemeS asked why the difference in phrasing, and Peter Groves says it makes no difference. But in fact (though Mr Grove is 100 per cent correct in IFAB's general attitude towards affecting play), there is actually a reason for this difference in phrasing.
In number 1 above, any attempt by the PIOP to actually play the ball (and by play it does mean attempted contact, not just running towards the ball) can "impact an opponent" even if that opponent is not in a position to play the ball. For example an attempt to shoot that just misses the ball but sends the keeper (five yards away) diving the wrong way. This "impacts" his action and leads to offside call.
In the second instance we DO deal with a PIOP who may just be running towards the ball rather than attempting to play it. In this case just impacting an opponent is not enough, he has to actually physically affect the defender's ABILITY to play the ball (basically by getting in the way somehow, as Peter Groves correctly states, just affecting the defender's mindset is NOT enough).
This is subtle stuff, but, as a large number of people have pointed out, by this reasoning, the Arsenal goal was NOT offside .