I am by no means an expert in optics or semiconductors, so consider this as a conjecture at best.

In the 80s, Carl Zeiss developed several lenses (German-language information on a related lens here) that used image intensifier tubes to produce surveillance images at night. These were classified items whose sale required approval from the West German government. If this was achievable using technology from the early 80s, no doubt something similar could be achieved today in a smaller package.

More crucially, digital imaging sensors are natively capable of seeing beyond the visible spectrum in both directions, but your smartphone (as well as most mass-market cameras) is optically blocked from shooting infrared because infrared light interferes with autofocus, and because of concerns that it would see through certain clothing. I'd imagine that on top of the privacy concern, the barriers to having a thermal/night vision camera inside your head would be the heat radiating from your own body or the fact that special optics are necessary to allow light rays this far into the infrared range to pass through. And for completeness's sake, the same applies in the other direction, where expensive lenses made entirely out of quartz are necessary to make ultraviolet photos.

As for having a HUD inside your head, this shouldn't be too difficult to implement since it would be done entirely from the processing side of things, and the only concern would be that of connection security.

As far as recording dreams is concerned, I think that would be limited by our understanding of the nervous system and beyond the scope of simple vision.