Granted I have not lived in the building in the past couple of years, I had no major qualms with 1036 N. Dearborn while living there. Although management changed a lot, and my neighbor was loud and noisy, but after a note on his door it subsided quickly.
I never heard of any crime going on in the building while living there and I found that the night doormen were good at keeping the questionable people from the White Hen moving along. Really nothing I can even think of terrible going on, not even in front of the building...the biggest complaint from our floor (8th, by the way) while I was there was some other tenant decided to put mothballs in the hallway, which left a disturbing pugent odor the rest of us had to experience.
The building is old so I expected rusty copper piping, but I guess as a daughter of a plumbing-firm owning parent, I found it easy to retrofit the fixtures with filters (the water in Chicago is so hard anyway, I would imagine most people don't drink without at least using a Brita filter from the tap). No issues with laundry/mail service/package retrieval/etc.
I lived on the inside of the building but accepted the lack of sunlight in exchange for cheaper rent. It had just been rehabbed and I was the first to move in after the remodel so maybe that's why I had no major issues.
The only thing I remember complaining about was my neighbor's dog (a beagle) who barked all day, which just made me wonder why a building composed of mostly studios, some one bedrooms, would even allow dogs over 25 lbs. Some of the people I saw in the elevators had large dogs (labs, pitbulls, etc) which I thought was almost cruel to be kept in a studio..