Examples of where Corsi Rel can lead us astray:
A. A poor territorial team
Let's take the Islanders, who according to Vic Ferrari's Time On Ice script, were 46.5% Fenwick in all even strength situations this year. We know they were driven back a lot. This is going to create a problem if we just look at one player's Corsi Rel with his Zone Start, because a player may have a positive Corsi Rel with a below 50% Zone Start - these two things together are assumed to indicate skill.
The other issue with the Islanders is their atrocious 4th line. Trevor Gillies had a woeful 26.4% Fenwick. Expressed in Corsi/60, he was -52.07. These horrendous results are going to skew all the Islanders' Corsi Rel numbers, because they pull down the team's total Corsi by a not-insignificant amount.
B. A team with lots of injuries
Take the Islanders again, where no defenseman played more than 64 games for the team. They also had lots of players going in and out of the lineup at forward - 10 forwards played 42 or fewer games last season for the Isles. Perhaps I'm just unclear on the meaning of Corsi Rel, but as I understand it, it compares a player's results to the players who are also on the team when he is playing. Depending on what lineup the team is icing, it may give a skewed picture, especially if that lineup is particularly worse or better than the lineup the team 'typically' puts out.
C. An excellent team
This is basically A reversed. A team like the 2009-10 Chicago Blackhawks, which featured 11 players with above a 50% zone start and most players with out of this world Corsi production, could make things look ridiculous. For instance, Dustin Byfuglien had a -5.4 Corsi Rel that year, but he had a 10.1 Corsi On. He was still probably an excellent bottom-6 forward, despite the negative Corsi Rel on a great team.
D. Quality of Competition
My colleague JaredL helpfully pointed this out, and I think he wrote it so well that I won't even change it: "Corsi Rel tends to exacerbate usage issues. If a player plays against tough competition then that means his team's competition when he's off the ice is going to be easier. That makes it a double whammy - his Corsi On takes a hit because of the tough competition and his Corsi Off gets a boost because of the weaker competition. The same thing applies to O-Zone Starts."
E. What are we really measuring, anyway?
We've mentioned before the thought experiment where we consider two hockey teams playing against one another with static lines - line A goes against line A of the other team, line B vs. line B and so forth. We know that hockey is a more fluid game than that - teams match up different lines against different lines, whether by chance or by choice, and players move around on lines due to injury and performance. Regardless, what exactly does the first line have to do with the fourth line? How much influence does the third line's play have on the first line? Corsi Rel assumes that that relationship is particularly meaningful.
I'm certainly not smart enough to synthesize Zone Start, Quality of Teammates and Competition, as well as Corsi, into one statistic that would comprehensively define territorial play. I'm hoping for that day soon. Until that day comes, we will be stuck with Corsi Rel - it's far from perfect, but in some ways it's still the best we've got.