Good points. Addressing separately:
1) On a phone that hasn't been jailbroken or rooted, I believe Snapchat notifies the sender if the recipient takes a screen capture of their message. This doesn't prevent it from happening, but it may at least make people think twice about it. If you're having a fling with a girl, and the girl sends you an explicit Snapchat picture which is intended to disappear after you view it, and the girl gets notified that you took a screen capture of it, she might go "What the fuck?" and you might not get any more nookie from that girl; for some guys, this might not be worth the risk.
More generally, of course you're right -- some pics will get screen captured. But Snapchat doesn't have to work perfectly for this purpose, it just has to work better than what people are doing now (sending texts which stay on your phone forever). What percent of explicit pictures sent by text message get deleted right after they get sent? Probably very few. What percent of similar pictures sent via Snapchat get deleted right after they're sent? Probably most of them. It's just an improvement, not a panacea.
2) It would be better if Snapchat let users set up end-to-end encryption so even Snapchat wouldn't be able to eavesdrop on people, and we wouldn't have to "trust" them. For now, all we can say is that it's better than using text messaging.