Some problems, but very accommodating
This is my 3rd stay at the Millenium. Hotels in Boston are not cheap and so when choosing, I base it on location and proximity to other things I want to see and do in the city. I am a "Bostonian" who moved to the outskirts of the city, so spending a weekend in Boston is a fun thing to do.
The location of the Millenium is adjacent to Fanueil Hall. Many of the rooms have a balcony which overlook Fanueil Hall Marketplace. By day this is a beautiful view and fun to people watch. Be warned at night.... it is very loud and raucous when the bars are letting out. My suggestion to the hotel is to install better soundproof glass. This did keep us awake from @ 1:30 - 3:30. There was a time we would have been part of the outside madness - but not anymore.
We had to change rooms 3 times. The staff was very accommodating with our situations. The first room was right after we checked in. When we walked into the room it REEKED of stale cigarette smoke. We later learned right below is a cigar bar and this was probably the cause. Our 2nd room was perfect - in the front of the hotel on the 5th floor. However, when we returned to the room from breakfast, the keys wouldn't work to the room. It was learned the battery mechanism in the electronic lock had died. While we waited for the situation to be rectified, we were offered a complimentary drink at North26 (the hotel's restaurant). Even though it was only 10:30 a.m., we took the offer! :-) The staff was very quick to accommodate us to another room on the 7th floor with the same beautiful view. 
Aside from the room mishap and the outside noise at night, this is a wonderful hotel. I would stay here time and time again.
It should be noted there is an additional $45.00/night for parking. Every hotel in the city will charge this amount, but if you're not aware of it up front, you could be surprised at the cost.