There are really only three effects in the films that make me cringe and look away: Legolas shield-surfing, Théoden's old-mummy to spry-warrior-king transformation, and the much-discussed Galadriel temptation scene. Interestingly, I think the latter might have been salvaged by decent audio (tip o' the hat to Fordim).
But FX schmFX. FX are simply another tool in the director's toolbox, one which can be used skillfully or clumsily. I commend Jackson on his extensive use of practical effects (i.e., non-computer generated effects): use of forced perspective and different scale sets and props to sell hobbits as hobbit-sized, for instance, or the building of the Golden Hall on an actual bluff in the middle of a rugged wilderness instead of on a bluescreen soundstage.
On the other hand, Jackson's deficiencies as a director -- which I think can all be boiled down to a lack of subtlety -- are as evident in the writing, in the staging of certain scenes, and in particular acting choices as they are in the use of visual effects. I don't think, in short, that taking CGI effects out of Jackson's toolbox would have significantly improved the cycle of films; on the contrary, I think that high-quality, mostly well-conceptualized effects (visual and aural) are one of the films' main strengths.
P.S. -- Before I'm pounced upon by Jackson devotees, let me say that I think he has many virtues as a director: an excellent design sense, good visual instincts, and an enthusiasm for his work which translates to the screen. I also admire that he has created a team and a working environment which seems to put as much emphasis on enjoying the
process of filmmaking as on the finished product.
I think his talents will better serve straight up popcorn fare like the upcoming
King Kong, though I'm a fan of the LotR films as well, for all their flaws.