This is my first version of the review. I haven't done any real editing yet. I'd like you guys to point out anything that would be worth touching up, and anything that might prevent it from being accepted as a review on this site. I haven't written a review for a game before.
Pretty good the only thing I can disagree with is your issues with regular battles. You get so many regular stickers outside of battle that you may as well battle to maximize your coin total(from perfect bonuses and the reward at the end of the level) otherwise you end up having to throw away stickers.
Additonally this means that you have more coins to buy Thing stickers and specific stickers(Hop Slippers) and for getting easy triple icons on the bonuses spinner which mean you can defeat all but a few bosses even without their weakness stickers because Things always do respectable damage and even with 1-3 regular Hop Slippers you do 10-30 in one turn based on the Spinner result.
While theoretically you could go without doing any optional battles(I haven't heard of anyone who actually has). Without them you can actually be a little low on coins and have less control over your inventory and battle spinner options. You're at a significant disadvantage if you avoid battles even if they don't provide EXP.
I disagree with your point about the Radiator. Firstly, it's in World 3 and the Snifit tells you you'll get stuck without it if you try to skip the bonus round. Therefore, assuming you're doing the worlds in order, as any first-time player should, you WILL have the Radiator.
Most puzzles involving Things are actually quite obvious. It's only that one that requires a specific Thing. Anything that requires scissors will also accept things like the Barber's Scissors etc. Anything that requires a hoover will let you use any of the three. (Usually. The exception is in World 2, but you aren't supposed to have any of the other ones at that point.) So no, the puzzles really aren't that cryptic, especially for people who grew up with games like Zelda 1.
Or would you rather have the other extreme - Skyward Sword and Fi's constant obvious-stating and hand-holding?
My Pre-Hooktail Pit Run of Paper Mario: TTYD without Mega Rush P! Playlist: http://www.youtube.com/playlist?list=PL5045EE00B4B9581F