Twilight Princess was a good game, a great game even, but by Zelda standards, it had a lot of weaknesses. What is interesting is that if you ask people which they like better, TP or OoT, a lot of people will reply with whichever game they played first. TP was very similarly structured to OoT, especially with the gameplay formula. Unlike the other console games, TP really had no major gameplay deviation that made it stand out.
The point that TP is linear is a very valid one. While all the games have to have some sort of linearity to point you in the right direction, TP's linearity felt forced. This is especially true of the second half of the game, where there was practically NO storyline or optional intermissions between the dungeons. TP lacked OoT's loose dungeon order, MM's freeroaming sidequests, and WW's explorability, becoming instead a "go here and do this" kind of game for pretty much the entire adventure. The formula was too set in stone and repetitive, as evidenced by the Light Tear sections having almost no variation other than geography, and no deviation at all from the "gather 3 items, find new thing to unlock" dungeon structure. The game relied too much on formula.
TP's story in general was rather lackluster in my opinion. Ganondorf's inclusion was very controversial, and I am among the people who felt he was tacked on and ruined the game. Zelda had almost no characterization, Zant's potential as an awesome villain was absolutely ruined, Ganondorf had no character development at all, and the entire storyline sort of disappeared for the second half of the game. The game's plot was beautiful in the first half, then completely fell apart.
Frankly, the entire game seemed like a world of potential that wasn't properly tapped into. The overworld was huge, yet nearly totally barren. All you had were enemy infested fields, and the largest city in Hyrule only allowed you to talk to maybe 5% of the population. Zant was built up to be a genuine frightening villain, and then he turned out to be an infantile lunatic. The Twilight Realm could have easily become something epic like the Dark World was, but instead we got Light Tear gathering, a task that became simple busywork after a while. The graphics were made for the Gamecube, and there was no time to tune it up for the Wii, and either way, the graphics are quite simply dated.
Now, having said all that, I will say I loved TP when I first picked it up. It was my second Zelda game; it was what brought me into the fandom. Looking back on it after having played other games in the series though, especially looking at TP's second half, I must say the game did not live up to its full potential, and certainly not the full potential expected from the Zelda franchise. As I stated earlier, TP was not a bad game by any normal standards, it was simply a mediocre Zelda title.