Check it right now and report back. Prepare to have your mind blown.
Out of my collection of over 100 GCN discs, I had 4 discs report errors (this process scans 100% of the disc, so it's more intense than simply playing the game. Theoretically, they might still boot-up - I didn't get around to checking that...).
One or two of them were super scratched up, so I wasn't surprised when my Wii returned an error (I bought them used). The other two games did surprise me though (they looked mostly fine - I even 100% complete Sonic Adventure 2: Battle back in the day).
So in my experience, GCN games are just as reliable as any other medium. Keep in mind, just because my collection works fine, there is always the possibility that the disc mastering process might differ in quality depending on where you live in the world.
One final note: While cartridges are supposed to be more durable, I do sometimes worry about their longevity. I had two Game Boy games (Pokémon Red, Mario Tennis) refuse to backup properly. A few of my Nintendo 64 games gave me trouble, but I eventually got them to work after much persistence. Point being, contrary to belief, they aren't invincible.
Oh, on topic: Wii U discs do feel
smooth in the hand.
Edit: Actually, now that I think about it, we
did have a lot of issues with the discs at work. We went through two copies of Mario Kart 8, yet they looked fine on the surface. It might have been the Wii U itself (we only had the one system). It didn't help that the discs and Wii U were kept in a very cold environment at night time in the winters (+occasionally dusty).