I run it with the console both plugged in and handheld. On a TV, I have seen stutters a few (ten?) times in twice as many hours of gameplay. Even then they weren't very bad. My screen is not scratched. I have no dead pixels. The game is the best I have ever played. It is absolutely incredible.
My personal opinion? Bad news sells better than good news; a glowing review is never going to be as "good" (widely shared, viral, etc) a review as one selling problems. (And for websites and Youtube, it is selling: selling their channel).
It's not an issue undocked (because it runs at 720) and the game looks fantastic. If you play docked, though, there's lots of performance stutters - look at a certain area, attack a specific enemy and framerate drops to sub-30 and it might stay that way for a few seconds.
That being said, it's a good enough game that you can ignore it and even forget about it, but it's always there. It's my only real issue with the game.
I bought the carrying box for it, then no scratch on the screen. Battery life is good when used in transport (forget about road trips of more than 3-4h).
The game slow a little down when there is a huge amount of grass, but it doesn't impede the gaming experience.
All in all, I'm really happy with my purchase and I don't get how so many people have so many issues with it.
The only time I can recall stutter was at the beginning when I started down the mountain. It was very brief, and I thought there would be much more to come. I'm about 15 hours in and have only made it to the first village. No stuttering or frame drops in this configuration since the very beginning.