How can I view my graduate applications' recommendation letters?

Is the university wrong? Almost certainly not. The only way to get a definitive answer is to hire a lawyer and sue them, if you have a hundred thousand or so that you can't think of anything better to do with. The probability that you will offer an argument that is so amazingly cogent that they immediately mend their ways is exactly zero. Also, it's quite possible that because you didn't waive your viewing rights, your professors wrote only objective, verifiable statements about your performance, or about what you did and didn't do, and that consequently your letters were almost entirely free of opinion statements praising you. And yes, the right way to do this is to tell your recommenders that you got dinged and ask them whether they think you should ask different people for letters next year, and/or how you should change your application strategy.

In order to have rights to see the letters, you must be an accepted and enrolled student at the school you applied to, not your current school.

If it is a state university, you might be able to apply to get the information under freedom of information laws. But I'm guessing it isn't.

For next time, an anecdote: When a friend applied to grad school, half of the schools required the letters sent directly and half didn't. He asked his profs for a letter to a school that was of the latter category and that he didn't actually plan to apply to. Then he read the letter. And then he suddenly decided to apply to the school of his choice.

You could also talk to the professors providing the letters and ask if you could get a copy so you can better plan your next application. Maybe the protocol for grad school is different (I never applied) but when I got professional recommendations from academic contacts they didn't give a shit about me reading what they wrote (in at least one case - though I'm sure they meant well - I was glad I read it before anyone else had a chance to).

(Plus people who write you a positive letter are a lot more likely to be happy to give you a copy, so you can at least eliminate some of the suspects).

Seconding stevechemist. At the large US state university I went to for grad school, students were allowed to see their letters after they were enrolled as students but not before.

Perhaps this question turns on what counts as an educational record under FERPA. It makes sense that, if you are not a student at a university, you have no "educational record" there. I applied to a ton of schools for grad school and law school, schools to which I was not admitted, and it doesn't make sense to think that I have records there that I am entitled to view. Can you imagine the burden on universities like, say, Harvard, that accept 6% of their applicants, if all the bozos who got rejected had a right to demand to see various elements of their defunct Harvard application file? It simply does not make sense to assert that you have a right to view a file at a university to which you applied but were not admitted.

I'm a professor, and though I'm not a FERPA expert, I encounter it and am familiar with it, at least how it's applied at my University. My understanding is that the definition of "educational record" that we use specifically excludes students that haven't been in attendance. Even if you have matriculated, you won't be able to do a FERPA request until you've begun to attend classes. For a more definitive answer, search for the University's FERPA guidelines; they're usually posted somewhere in the website. It seems to me that the waiver is meant specifically to shield recommenders from the FERPA requests of students after they matriculate -- it's moot in the case of someone who doesn't get in.