What is the most "looked down upon" Broadway show?

Simply because many who consider themselves "serious thea-tuh people" look down upon shows that have an ardent, somewhat crazed bunch of fans. Next to Normal also gets the stink eye from many who consider themselves afficianados.

Most composers, lyricists, and bookwriters would kill for a show that becomes a phenom, but so few do.Therefore many like to "poo poo" those that do as somehow being so pedestrian that masses could so easily become enthralled.

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I'd add any Disney, jukebox, or otherwise "corporate" (aka movie-based) shows as being looked down upon, too. Personally, I enjoy those shows just as much as anything else. The fact that a show is "fluffy" does not make it bad.

Right. Honestly, as long as a show is actually good I don't care what the source material is be it book, movie, etc.

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Many (but by no means all) shows that are hugely popular with the masses seem to achieve this by "dumbing down". Wicked, for example, has bright things that flash and a cherry picker. People go nuts.
However, artistically it's pretty dire. The book is a mess, the score is forgettable and the choreography just isn't.

And that's why people look down on these shows.

Mamma Mia belongs in this conversation.

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Definitely Cats.

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History Boy illustrates this phenomenon perfectly- someone told him the way to look smart is to express his superior opinions about a popular show, and he did it flawlessly: Notice the way he puts forth his opinion as if it were fact: "artistically it's pretty dire. The book is a mess, the score is forgettable and the choreography just isn't."

PERFECT! Gore Vidal would be proud!

Incidentally, if it was so easy to write a book as popular as "the DaVinci code" Gore would have done it years ago!

Oh I'm sorry, I forgot that every mention of art must be prefaced with that magical pass, "in my opinion".

I believe there is a level of objectivity to art. Yes there are preferences and tastes, but there is a standard of quality.
To illustrate, if I were to give you a drawing I'd done, made using my own faeces daubed on some canvas and say, "It's a bunny", most would think, "Hmm, this isn't very good. It looks nothing like a bunny, though the similarilty of smell is remarkable."
Similarly, if I gave you a still-warm manuscript of "my new book about the adventures of some courageous field mice trying to bring down the evil forester", and you read it only to find page after page of description of the aforementioned "Runny Bunny", you would probably again think, "Well this is no good at all - there's nothing about some plucky mice and the forester is nowhere to be seen."
You might very much enjoy reading it, but objectively it is not good.

I think the same can be said of musical theatre. For instance, the language used should be character- and time-specific (unless it is deliberately incongruous, like in Spring Awakening). Sondheim dislikes the lyrical quality of 'Tonight' because he says no teenager at the time would speak like that. He sees it as "bad" because it is, for this piece of musical theatre, inappropriate.
In Wicked, the language and music seem to have no basis in character. In one scene, the characters simply have a conversation set to music with nothing lyrical about it. Next second, Elphaba sings, "my road of good intention led where such roads always lead" in a voice completely unlike that used elsewhere in the show. There's no consistency.

I could go on, but you may have stopped reading by now. I hope I've been clear.

Theatre is very subjective.

There are some people who love Billy Elliot but hate next to Normal.

Adore Little Mermaid but hate Beauty and the Beast.

Cherish Shrek but cannot stand Mary Poppins.

Abhor Spring Awakening but relish Fela.

Worship La Cage Aux Folles but feel repungance for A Little Night Music.

Abominate Come Fly With Me but feel enchantment for 9-5.

Carry Armour for Color Purple but execrate Dirty Rotten Scoundrels.

Have fervor for The Pirate Queen but feel aversion to Les Miserables.

Repugiate American Idiot but have piety for Mamma Mia.

Etc etc etc etc etc.................

As for myself I try to enjoy every show for what it is and on its own merits, it's that simple.

So there are no "good shows" or "bad shows", just ones you like and ones you don't?

That would be nice, but I really don't think it's true.

I gotta agree with Joe. What makes a good or bad book? There are scholars who will say Hemingway was one of the best writers ever and there are others who will tear him down. Yes, there are standards, but I don't know what they are in musical theater and I WOULD like to know how to properly critique a show in a scholarly manner.

If there are good shows and bad shows why do good shows fail? Why do bad shows succeed? If the music in Gray Gardens is so great why don't you like it? Why do some people hate broccoli- it's Sooooooo Good! AND good for you!

Because it's opinion and perception and personal taste. There is no such thing as empirical superiority.

Good shows can fail for myriad reasons - the public may not take to the subject matter or find the score or book too challenging. There are many who go to the theatre purely to be entertained and so enjoy shows like Legally Blonde and Wicked - nothing is complicated, nothing is difficult, you can just shut down and enjoy the spectacle in front of you.
Conversely, there are shows that I believe to be brilliant like Passion or Sunday in the Park with George that can be very intense, complex experiences that some would prefer to avoid.

As I said before: I don't think art is all "opinion and perception and personal taste". As a genuine question - do you really never say, "You should definitely go and see Gypsy, it's a great show!"? Must it always be, "You should definitely go and see Gypsy, I really enjoyed it!"?

As for Grey Gardens, I wish I knew. Something about it fails to keep me, but I do come back to it every so often to see if I'm ready to digest it.

And broccoli is delicious.