The speaker in this poem is someone living in the present (the present then was the early-mid 1960s), in South Boston. He seems to know the place and its history pretty well, and it's safe to say he's lived there for a while. We see him as a young person with his nose against the aquarium glass, then later reflecting on WWII, and then we see him in the present talking about the construction on the Boston Common, and the development of Boston.
This speaker seems to praise Shaw and the 54th regiment, but he is more critical of present-day Boston and what has happened over the past century. He's definitely an opinionated fellow, but he won't say outright just what's on his mind. In this way, Lowell leaves space for us to figure out how we feel about what's presented in the poem without the speaker's ideas or feelings crowding us out.