Picture messages fail to certain people with invalid destination address. Then the group messages won't send unless I send them as individual texts. Very frustrating.
Make sure your mobile data is turned on for all MMS (which includes group messages).
I am having this same issue! I got my S3 in December & it has worked fine until about a month and half ago. . .around the time of latest software update! I can not send MMMS messages (group texts, pics, videos). It doesn't matter if I am on wi-fi, 3g, 4g LTE. It does not send!!! And I am getting pissed. Help Verizon!!