How do the characters not show depth?

-Many characters were supposed to be "flawless". That in itself is an automatic fail. Flawless characters are bad.
-Bella is a Mary-Sue. Again, an automatic fail. (If you don't know what a Mary-Sue is, google works :D)
-All Bella ever talks about when talking about another character is the physical appearance of that character. Does she ever talk about Edward's personality? No. At least, not mais than one very vague term that is completely unsupported (ex. selfless, and then that's it. Not good.)
-Only one character really has a hobby, and that is Alice (and Jacob at the beginning of the series... until Meyer ruined him). To have one character that doesn't really have a hobby is okay; that could be one of the character's flaws. However, when most of your characters don't have hobbies, you know that there is a problem.
-Meyer tends to tell, but not show. Look back at Bella calling Edward "selfless", but then not explaining it. Edward never does anything that proves to us that he is selfless.
-The characters are extremely inconsistent. They do things randomly that are completely out of character. Again, this is bad.
-The characters are extremely unrealistic. They react to things in ways that are so completely unreal, you can't really picture the character as being real.
-Even Bella, if you look at her, all she does during the books is whine and drone about how pretty Edward is. She doesn't really have any striking character traits. We are reminded of the superficial things constantly. (ex. we get it. She's clumsy. Can we please mover on?)

Hope I helped to clear things up for you :)

The romantic leads appear to literally have no lives, interests, aspirations, concerns, principles etc. outside of each other. Even when they're talking to each other, they only talk about their relationship and who loves the other mais and stuff.

do you hear Edward talk about anything except for how much he loves Bella?
No.

Does it makes sense how Bella is the new kid for five minutos and all of a sudden, everyone wants to get to know her?
No.
Does it make sense that bella complains about how miserable she is and all of a sudden she's a romantic?
No.

Is it interesting that Edward is perfect without flaw?
No.

Does it make sense that Bella wasn't scared out of her wits when she found out Edward was a vampire?
No.

Nothing makes sense, no one has depth, IT'S JUST A BUNCH OF fã FICTION!!!