Should I waive my right to view my recommendation letters?
Among the faculty members I've known (at US research universities), there's a widespread feeling that recommendation letters should be completely confidential unless the writer chooses otherwise, and that viewing them using FERPA is unethically taking advantage of a legal loophole. Almost all the students check the waiver box, and if someone doesn't, then the letter writer is more likely to assume it was by accident than on purpose.
In this context, my advice is:
You should always check the box. If your recommenders believe you may look at the letters later, they will probably write weaker, vaguer letters. (For example, the most compelling letters often involve comparisons with other students, which may be omitted if you'll be reading the letter.)
If you are not checking the box on purpose, you should say so explicitly. If you do this silently, people may assume it was an accident, and then if they learn later that you viewed the letters, they will be more offended than if you had announced this plan in advance. (And they may actually find out, since the staff who handle your request may find it troubling and leak the information even if they aren't supposed to.)
You would learn less than you might expect from looking at the letters. It's remarkably hard to judge letters out of context, without having seen other letters from the same people, and it's not likely you'll discover a clear reason for your rejection. If anything, it might mislead you: you might decide that Professor X was damaging your chances by being insufficiently enthusiastic, without realizing that Professor X is never enthusiastic and in context this letter was viewed as very positive.
I think the fundamental worry many students have is of a terrible letter, a single letter that ruins what would otherwise have been a successful application. This can happen, but I see an example only once every few years. And even in those cases, it often looks like it should have been predictable to the applicant. (For example, if you have had difficulties with someone in the past but things seem better now, don't ask for a letter without a serious discussion of how they think things stand now.) So I wouldn't worry too much: the chances you could dramatically improve your application by substituting a letter are small.
The secret to getting a good letter from someone is making sure they're going to write you a good letter before you have them write one. You should never need to look at a letter someone wrote for you, as you should basically know what they're going to write without ever having looked at it. In most cases, if someone doesn't feel comfortable writing a 100% positive letter about you, they'll let you know when you ask them and recommend you get someone else to write the letter.
With that in mind, it is definitely better to forgo this choice, for the reason you suggested... people will likely feel more comfortable to write freely and honestly when they know you won't read it. Regarding the procedure, I'm not familiar with the mandate, but if it is a US mandate, then they'll probably show it to you after a lot of waiting. It is definitely uncommon for someone to ask to see a letter written about them, and it likely would be looked down upon.
You should definitely waive access to your letters of recommendation. If you don't, the people reading the letters have reason to suspect that the writers, knowing that you might see the letter, would omit (or at least soften) any negative information that they would otherwise have included. As a result, your failure (or refusal) to waive access can weaken the letters in the eyes of the readers.