I don't agree that applying early can be detrimental. I think there are few cases where applying early can be harmful. With all due respect, borderline or longshot candidates who apply early and get deferred would probably be rejected much later in the cycle or deferred regardless.
I'm not sure what logic there is to the argument that if you weren't sufficiently impressive early on that if you had applied 2 months later, after they saw all of those other applicants, you would look better.
I'm not sure where I read it summed up this way (perhaps Ivey), but this was resonant for me:
When you are the first handicapped minority to start a nonprofit group, you are an exciting candidate. Three months later, you will be the 15th, not nearly as exciting and possibly even old hat.
The point is, early helps. I would point out three obvious advantages:
1) You are less likely to be compared to other similar candidates and, thus, stand out with your own voice. You are also likely to be more impressive than after admissions has seen a number of similar applicants.
2) Admissions people are fresher and liklier to give more time to your application in the early phase. Think of how you would address files the first week or month of application season. Consider, then, how mind numbing it would be come March when people are much more likely to look like a set of numbers. I think a more thorough look helps because it means your PS and recs will speak louder.
3) It looks like you have your *&^% together. Being organized and on top of things is likely to give you a slight edge, especially if you are otherwise unremarkable.
To summarize just how big a deal this is in my mind, I would also add that probably the foremost piece of advice I give people in applying to law school is: apply as early as humanly possible - September if you can. I don't even offer this with consideration of how it may increase chances; I tell people this because the agony of waiting can be greatly ameliorated by having your apps in as early as possible.
If I had been done applying by October 1st instead of December 1st, I'm pretty sure I'd be into the same schools (or better) than I will end up in at, but I probably wouldn't be waiting around, going psycho over my pending applications at this point.