The protection will probably consist of more than one element. Historically, systems have had two types of protection: one aimed at developers and/or publishers, the other aimed at preventing the creation of usable copies.
I haven't seen a GC in action, but I wouldn't be surprised if it reads a Nintendo logo graphic from the disc and refuses to run if it doesn't match a graphic stored in the BIOS - this is the scheme used by Game Boy. This is done because the graphic is (presumably; I know there is some case law that might suggest otherwise) protected by copyright, and thus it's impossible to legally publish GC games without a license from Nintendo because you would have to infringe on their logo copyright. They might use a proprietary filesystem as well, similar to 3DO and Jaguar CD, which would explain being unable to read files or filesystem information. This isn't really a copy protection measure since you don't need to know how the filesystem works to just copy the whole thing; you only need to know that if you want to create or modify a game.
As for copy protection, they really don't have too many options. I suspect it's some proprietary element added to the format - this would most likely be in the form of something that doesn't break physical compatibility with DVD, such as a modified format for error correction. This could also be in the form of a weaker violation of the accepted standard confined to a limited area of the disc, similar to what PSX uses. I highly doubt that it's just the size, as 8cm media has been in the DVD-R standards for years, and consumer DVD burners are really coming down in price (lower end now is somewhere around $350-400US). It's possible that they use something related to the CSS system, since consumer burners and media are intentionally crippled to be incapable of writing those parts of the disc (actually, the authoring drives can't either, but that may change eventually).
In addition, the BIOS ROM may be integrated into the CPU package (so far I've seen no indication of a seperate BIOS ROM package on the board). If this is true, then circumvention will probably take a while, as it would require intercepting the signal from the reader and modifying it.
