I have a very skewed and non traditional opinion about the series as a whole (long story short, I only liked Super Paper Mario: not a fan of the first two games and I don't want to play play Sticker Star or Color Splash), but after completing Origami King, I can conclude that it's a fine game. I actually really like the puzzle based battle system and the fact that there's no EXP system (it's something I've long wanted gone from RPG's). I got stuck at a couple points, mostly because I was just being stupid, but overall I got through most of the game without any hiccups.
Do I think the game has significant issues? Of course, but a lot of what I found wrong with the game really has nothing to do with it not being a "true" Paper Mario game.