I (and many others) have experienced several issues with the wpautop function indiscriminately adding p tags and br tags throughout my code.
I've had to turn this function off in my functions.php file. However, I think the randomness of the wpautop throwing tags around is a bug, and should be looked into for future versions. Turning the functions off, turning off TinyMCE, and disabling basic WYSIWYG editing defeats the ease and friendliness that WordPress is known for and prohibits newbs from using an interface without html knowledge.
I don't recall prior versions of WP throwing random tags and am at a loss as to why this bug has been introduced. Is there perhaps a reasonable explanation as to why it was, and when or if there are plans to get it fixed?