Quick Answers

I am a professional illustrator, and I've just started writing my first children's book, which I plan to illustrate as well. I've seen different advice on how and what to submit to publishers and agents as an author/illustrator. Some say you should submit a dummy book, and others say you should submit a standard manuscript with a few example illustrations included. If a dummy book is the way to go, do you prepare it as closely as possible to what you picture the final book to be? (layout, typeface, design, at least mock-up illustrations on each page, etc?) And if it is preferred to submit a standard manuscript, in what manner do you include the illustrations? Do you just include a few prints paperclipped to the manuscript, or do you try and show where in the story they fit, by laying out some text with them?

I would recommend manuscript pages, a sketch dummy (don't spend time worrying about type and design), and a couple samples of finished illustrations.

My first question is, as an editor, what do you want to see in a cover letter from an illustrator? I've seen plenty of advice for writers on how to structure a query letter, but there seems to be little advice for the illustrators. Is there anything specific that should or should not be in an illustrator's cover letter? Does the illustrator need a cover letter at all?

Not really. If you're just sending illustration samples, most of those come labeled with the artist's contact information and that's it.

My other question is about formality. In sending out packages of art samples/cover letter to publishers and their art directors or editors, how important is it to have typewritten addresses or address labels rather than handwritten?

Unimportant.

Again and again I find myself reading a book which I bought based on reading the cover blurb, only to find that the story, and sometimes even the genre, has been completely misrepresented. For example a book I bought last year had a blurb which described a story about an archeologist finding an ancient sword in Jerusalem which may have been the sword of Mohammed and that finding it may change the world, the title was even Sword of God. The sword appears on the first chapter but immediately after finding it (as in still down in the tomb covered in dust) the character is drawn into a (rather cliched) espionage adventure in which war crimes in asia are uncovered. I spent the whole book wondering when and how the sword would be worked in and it never was.
Now, perhaps this happens because, like cover artists, blurb writers read only the first chapter, but I think it has to be a deliberate marketing ploy - after all, you can't return books after you've read them (at least not in Australia) so perhaps some publishers don't care about disappointing/lying to their readers as long as the purchase is made.

Seems awfully stupid to me. I mean, sure, a publisher might farm out its covercopy needs to a freelancer, but then how does the editor not read the copy and realize it's wrong for the book?
That's sloppy, sloppy publishing. In this country, people can and do return books, but if you don't have that option you can at least stop buying books from the publisher who can't reliably tell you about the books they print.

Do you know of any mainstream publishers that accept electronic submissions? Very few do currently. Why do agents want to go green and publishers prefer snail mail?

Do you mean mainstream publishers that take electronic submissions from agents? That's everybody. But if you mean mainstream publishers that are open to unagented manuscripts and take electronic submissions, no.
Agents get a lot of email in the way of submissions. People at publishing houses get a lot of email simply generated by the rest of the company they work for. Both agents and publishers battle a stormtide of incoming email, but if publishers had to deal with the email they already get and an ocean of submissions emails, we would be sunk. (Also our computer servers can't take it.)