Most of the red are clearly college dorms, or in student areas. For example, Bay State Road next to Boston University, or Pratt Street in Allston. There is a block on the border of Roxbury and Dorchester near Shirley Square which is marked red. I actually happened to walk by this area the other week, but I don't recall anything out of the ordinary. It is possible that this is just an error in the data. Some of the other red blocks are probably flukes as well, as they are marked as having only a few housing units.
I think the most interesting feature of this map is that the densest areas of the city, such as the North End and the Fenway, are also the least overcrowded, as well as being pretty nice places to live. This is an obvious fact if you stop to think about it, but many people and planners make the mistake of confusing density and overcrowding. Or they even conflate it into one concept: "highdensityandovercrowding" as Jacobs noted. Well, it turns out that Boston has many great examples of how density and overcrowding are completely different.
The trouble with using population/housing units is that overcrowding isn't normally measured in those terms, because there is such a wide variety of housing units. Typically it is measured in units such as persons/room or per square foot. But I don't have those measures so I will have to make do with this as a proxy. I would guess that in some places, there are more families living together, and those areas will appear to have more people/unit, but that is not really a problem. This probably explains some of Dorchester's higher numbers, for example. On the other hand, in place where people tend to live alone or with a roommate, the ratio of people/unit approaches that of people/room, and therefore the measure becomes more accurate.