We were a bit worried over the last reviews on Alessandros apartment (especially the one about heating) but it was and we had no problems.
As others have said the location is amazing, it's close and walking distance to most places. We even walked to Colosseum and Vatican City. So one chooses this place for the location primarly I would say.
When we stayed there, they were doing renovations of the buildings facade so you couldn't see the view of the Hadrianus building outside, but it didn't disturb us personally.
What should be noted is that the apartment is a bit smaller than one can get the impression from the pictures. The kitchen is really small. It is also an apartment that seems only be used for renting, so the small things that you find in a home were people are living are missing.