I've not had an issue sending texts messages through AT&T so long as there's a signal, but I've had a great many instances where people I'd send messages to would respond telling me that they received multiple copies of the same message - sometimes if was just one duplicate, other times it's been many (someone once told me they received the same message seven times despite the fact that I only sent the message once and it seemingly went through immediately).
Likewise, when someone sends me an MMS I will often times get the message twice.