The movies themselves hold up pretty well as one grand epic split into three parts (the Extended editions only improve upon this).
Parts will always fall by the wayside and could have been done differently and everybody has different parts they don't like.. i could have used less comic relief Gimli which i attribute to the insane notion that all action movies need someone funny to lighten the mood.
Could have also used less ridiculous Legolas stunts.. we know that Elves are far more agile than anybody else but surfing down stairs on a shield while shooting Orcs?
I love the small details that show these differences such as Legolas walking on the snow while everybody else sinks in.. it was a bit more subtle and not on the nose like some other scenes with him.
Digital effects also look a bit wonky sometimes, especially when they used the mass software to show huge amounts of troops.. especially noticeable in the final battle at the Gates of Mordor when Sauron dies and his troops are fleeing (though the team did a brilliant job often finishing the effects just mere weeks before release).
I especially love the first movie. Fellowship of the Ring has everything in it.. establishing the characters very well, action, fantasy and huge emotional moments ( i nearly broke down twice when the Fellowship mourned Gandalf after he fell in Moria and when Sam declared his friendship to Frodo at the end of the movie "Don't you leave him Samwise Gamgee!"
No matter the faults or deviations from the books i still love these movies because i'm a huge fantasy fan and this is one of the biggest epics in that genre done very well.