Good things
Story--At least in the beginning and the very end of the game. A little after the middle, the story felt like it dropped off - it suddenly became much more relaxed.
Mechanics--I loved all the different possible sword moves, and how Link could swing his sword while running. The wolf mode was also cool, but it could have been used more.
Camera control--After playing Twilight Princess, I played Ocarina of Time again, and I kept reaching for the C-Stick to move the camera only to find it didn't exist on the N64 controller.
Overworld--I like the more open overworlds that let me just play around with various items in a large area. Hyrule Field could have had a few more enemies and NPCs though.
Dungeons--The dungeons were cleverly crafted for use with the item that Link got in it. The boss battles at the end of the dungeon usually required clever use of that item too.
Music--Twilight Princess has one of my favorite soundtracks in the whole Zelda series. The music sets the perfect mood and never seems our of place. It is also quite interesting to listen to on its own.
Bad things
Item slots--Because there were only two item slots, I found myself going into the item menu very frequently. It's not that much of a hassle to bring up the item menu, but I felt it interrupted the gameplay too much in some of the more item heavy areas.
Ending dungeons--In a Zelda game, I usually expect the last dungeon or two to give the most mind-bending puzzles in the game. Some items were rarely used after the dungeon they were obtained in. I expected to have various puzzles that required careful use of all or most of the items Link had obtained.
Mini-bosses don't come back--I enjoy fighting the mini-bosses over and over, and in many Zelda games, they return again and again. The only mini-bosses that return are Darknut and Aeralfos. Some of the mini-bosses have a story behind them that wouldn't let them return, such as Ook and Dangoro, but most of the others could easily be fought again in the harder dungeons. Returning mini-bosses would also have upped the difficulty level (which was a little too easy).
Linearity--Linearity can be good or bad depending on how it's used. The beginning of the game was perfect for being linear. The second half was just as perfect for being non-linear, but it also was linear. The three dungeons after Arbiter's Grounds didn't have to be in any specific order. In fact, I don't think the items obtained in the dungeons after Arbiter's Grounds are needed in any of the other dungeons (except the last two). Ocarina of Time was set up in a similar manner, but it didn't have much of an order for the later dungeons, and I think it was better for it.
Hidden skills--The hidden skills were an excellent idea, but I don't think they were used as much as they could have been. The last Ganondorf battle would have been much better if it required the use of more of the hidden skills.
Sorry for the long post. Twilight Princess is a game I really love, but one I also like to rant about at times.