I have a similar problem. Using Handcent...first it said the person's number was not authenticated with a screen popup. On all the phones I have owned I have never seen this message. Then, I got the "rotating circle" that showed it was trying to send the picture, but it never did. It did ask me if I wanted it re-sized, which I said yes to. Think it makes any difference on what the settings were on the phone when the picture was taken?
I had this very problem last week when I first got my phone. It drove me crazy. I couldn't send or receive texts with pics in them. I contacted my provider and explained the problem. They were able to walk me through the settings and add some new settings. After that it worked perfectly. I changed carriers before I got the new S5 (which so far I love).
I've had this problem for a while using go sms pro. It started with my moto x so I stopped using it and went with the stock app. When I got the S5 I decided to go back to Go SMS and again now all i get is a loading arrow and it never sends, after a few minutes it just gives me an error notification. I know there's a lot of options and I've tried them all and I get the same issue. It's just a weird thing, not a big deal for me I just go with stock or hangouts as default sms now.