I've been reading applications. And reading some more.
And I have some advice.
1) Follow directions. Really.
2) When you write a business letter, it's customary to put two headers on the letter. (And make no mistake, a letter of application is a business letter.) The top one, on the right if you prefer, should give your name and address. Yes, even if there's letterhead, unless it's got your name, put your name.*
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Then the second header gets the name and address of the person you're supposed to address the letter of application to.
This, this you should have learned in high school. It's the genre of the business letter, and if you choose not to do it, choose knowing that your letter will stand out, and not necessarily in a good way.
3) Address your letter in some way: Dear Search Committee, Dear Department Chair's Name, To Whom it May Concern, whatever. But address it in some way. Again, this is a genre thing, and if you choose not to do it, choose knowing that your letter will stnad out, and not necessarily in a good way.
And yes, you should have learned this in high school.
4) Start off with some sort of introductory phrase. "I'm writing to apply to your position in deep-water basketweaving" will do, if that's what you're applying for. Don't just start out saying that "I rock soxors as a basketweaver!"
Again, this is a social custom thing. You can choose not to do it, but if you do, you should make that choice knowing that your letter will stand out, and not necessarily in a good way.
All these things stand out more because my department colleagues and I don't teach basketweaving. We do pretty much all teach composition and writing, and if you haven't learned the basic generic skills of writing a letter, we're going to think that you won't be able to teach writing well, or write appropriate letters of recommendation, or write appropriate letters for other purposes. And you might be surprised to learn that we'll expect our new colleagues to do all of those things.
Edited to add:
* I've been corrected, and told that you don't need the header identifying yourself if you've got letterhead. Thanks, folks.