I've worked DT since 1995. First let's define DT, roughly it's boarders are Jefferson St to South St to Mill Street to High St (these don't necessary all connect but you get the idea - basically a half mile of the governor's mansion in any direction). DT is not unsafe at all. A few crazy homeless guys, my favorite is the one who wears the cape, but he's hit or miss, haven't seen him in a while. There's an older gentleman with a gray beard who's 100% harmless. About one month ago at 0600, I did the encounter the crazy mentioned above who stands in the middle of the road trying to hit cars, it was at the intersection of Pearl and West.
I've never had a problem in over 30 years, I've parked all over DT and never had a break in (I drive older vehicles and leave nothing in view) and I'm gone before 5pm 99% of the time. Never had what I consider a dangerous encounter (unless you count the incident above), but I do keep my head on a swivel.
I don't recall a "shoot out" at any of the three roundabouts on Capitol (one in front of the Fed Bldg, one in front of the Region's Bldg - I believe that's what it is called now - and one in front off the governor's mansion).
There were many more car break ins/thefts in the 90s, but there were a lot more cars and people DT then (more opportunities). I'm not DT at night or on the weekends, but I know there's been issues at the "Daiquiri" Shops and there's often shootings in association with the St. Paddy's parade.