I'm pretty sure that what you are seeing is due to an issue between the new webmail system and Safari that is preventing you from entering text. You can try using the mobile version of the MyVerizon site (pretty sure it's at m.verizon.com) or you could set your iPad up to retrieve your mail from the mail server using POP3 access. Just be aware, POP3 access will by default erase your e-mail from the mail server after it is download onto the iPad!
