What is a red pixel appearing in the same spot on every photo, and how do I fix it?

It is called a stuck pixel, because it seems to be stuck all the way on in every image. To be more precise, it a red pixel that seems to be stuck all the way on. When the camera or RAW convertor program converts the information from the sensor, the high value of that one pixel is also causing the surrounding pixels to have artificially high red values assigned by the interpolation of the demosaicing algorithms.

A dead pixel is just the opposite: no matter how much light strikes it, the pixel reports no light. Sometimes a dead pixel will be masked by the interpolation of colors surrounding it being assigned to that pixel.

The only way to fix it is to do what is called pixel mapping to tell the camera to ignore the signal from the stuck pixel. Some cameras do automatic pixel mapping "hidden" in other routines. With Canon, for instance, if you use the manual cleaning option to open the shutter the camera also creates a new "hot pixel" map. If you leave the camera in Live View for a few minutes first so that the sensor is heated up, more pixels will be mapped out. You can then let the camera cool and do it again to map some of those marginal pixels back into active use. A new pixel map is also generated each time the firmware is updated. Other cameras have user accessible manual pixel mapping. Some require a trip to a service center. Short of that, you could use a dust delete tool or repair tool to mask the hot pixel in each photo, but that is a tedious way to go.