I hope my discovery can save someone else from the many hours I spent figuring out this stupid issue. (I won't detail the various ridiculous contortions Verizon service put me through before **I** figured out what was going on myself).
PROBLEM: Some of my text messages were being successfully sent but never delivered (you can tell this has happened if you look at your SENT log. Successfully sent messages show a green "up arrow". Successfully delivered messages show a green check mark). Also, around the same time, I would occasionally get an "invalid destination address" error when trying to send a picture message.
SOLUTION: It turns out my "problem" was that if, when sending a text or picture message, you type the ENTIRE "nickname" you have for the person (from your contact list) and then just hit OK instead of using the arrow key to select the nickname entry, the software isn't smart enough to resolve it to the entry in your contact list. So for example, if I have a contact that I have given the nickname BOB, if I type BOB and then arrow down to select the BOB entry that is shown to me, it will resolve it to the correct phone number from my contact list. If I type BOB followed immediately by pressing OK, it is not smart enough to realize that BOB = BOB from my contact list, and apparently thinks that I'm trying to send it to an email address of BOB. So those are the messages that get sent but never go anywhere. So you ALWAYS have to "arrow down" to select the contact list entry, even if you type the entire nickname.
(I'm sure Verizon would call this a "user error". I call it an "idiotic interface error" 
). Hope this helps someone!
