I seem to have to dust-like speck on my Sony Cybershot S950's lens, but it appears randomly every few pictures. Could something be going bad internally?
That sure looks like sensor dust, for which I'd recommend seeing the answers in the Best way to clean a DSLR sensor thread. The spot may appear "randomly" because it only appears when you're using a narrow aperture.
That said, it seems you don't have a dSLR, thus no interchangeable lenses which are what usually causes the situation where dust can get inside the camera body. I suppose it's possible that dust got inside the camera through some other way although I think that's a fairly rare occurrence.
If the camera is still under warranty, it's worth a call to the manufacturer.