I agree about the Mary Sue problem. I liked Arnold in the first season when he acted like a real kid.I think it was only season 1 where Arnold was written realistically and with flaws. I remember the "Heat" episode as a kid and how he completely spazed out on the Jolly Olly Man. "NO ICE CREAM , NO PEACE !" LOL. That was one of my favorite episodes as a kid; later seasons Arnold would've never done something like that.
Despite my beef with the Catdog being overly sadistic far too often, it's still one of my favorite nicktoons.
You got a point about the about the Doug character. In addition, I agree about a blank character with no flaws. How is that relatable?
Early Arnold was fun since he kept this sort of eccentric, spacey quality to him. Even when not acting flawed, his moments of clarity had this sort of amusingly vacuous, matter of fact demeanor to them. One of favorites quotes from Arnold.
"Wait, what's it like to fly?"
"Eh, it's okay."
I think that's one of my positive biases since I feel a good character can emit their defects from both their good and bad moments. A character that just changes their whole personality according to either direction feels more inconsistent than fleshed out (eg. characters falling to a Compressed Vice aren't really anymore flawed because of it, they just break character). This is important when writers try to flesh out a character, they need to make a 'quirk' for the character for them to work.