This has been an issue on Android/Carriers since I had my OG Droid. I saw it on my Galaxy Nexus and see it on my Note 2 too. Every time it happens to me, I notice that it always happens when the other person sending me the message is on a different carrier than me, so I think it's carrier related, not phone related. I saw this because my mom can send me a pic from her iPhone 4 on Verizon and it displays as a pic fine. But I have a friend in school with me with an iPhone 5 on AT&T and when he sends me pics from his iPhone, they open as video messages.
I use Handscent SMS and it seems to alleviate the issue for most messages. But for some reason my friends iPhone 5 on AT&T still play as videos even when opening them in Handscent. I have seen instances where the stock messaging app plays a picture as a video though, then Handscent will open as a normal picture.
So it may be a combination of phone/carrier differences. I've searched this issue many times for the last few years and never find a definitive explanation for it.