There is actually a rare condition called Tetrachromacy caused by a mutation of genes in the retina that let a small number of people see into the UV spectrum. Attached is a link to a BBC article about one such person.
As to your question about how useful this would be the answer really depends on your point of view. According the the article the main effect is that the people concerned see a large range of colors in objects that normally don't appear to be very colorful to people with normal vision.
This is because the objects concerned don't reflect much color in the normal spectrum but do in the UV. An example given in the article was a gray/dull colored pebble pathway that to the person with Tetrachromacy sparked like multi-colored jewels.
So the chief advantage would I guess be that you would see more color/beauty in the mundane world. Which I would argue falls under the heading of 'Nice to have' rather than Useful to have. This would also explain BTW why the mutation is not more common, it doesn't bestow any particular evolutionary advantage to a carrier of the mutation but at the same time it doesn't seem to be disadvantageous either so there's no real evolutionary pressure selecting for or against it - at least in humans.
On a societal level I think it would be a 'cool' (good adaptation) because the world would be more beautiful/colorful for everyone but that seems to be about the limit of its impact.
Lastly as a frame challenge - I would suggest mutations/adaptations to the eye that gave us better night or distance vision would be more useful than one making different spectrum of light 'visible'. That said seeming into the IR range would be difficult. As I understand it the size of the human iris would have to increase considerably in order to capture enough IR photons to be useful. (Someone can correct me if I wrong on that last bit!)