There was that police precinct they broke into and burnt down near the beginning. Also that federal court they tried to break into and kept tossing molotovs inside, which resulted in Trump deploying the national guard. Plus a number of government buildings they occupied peacefully.
BLM riots were less bold, but there was plenty of opportunity for bad actors to do stuff because of how long they lasted.
From what I've seen/read from back then, at least, in DC the truly violent parts (e.g. torching buildings) were at night (i.e. not during hours of operation). To me that makes a difference, especially because the breaking in to the capitol was during the reading and consideration of electors for the presidential election, while members of congress (and the VP!) were gathered together.
(Not excusing torching buildings, mind, though I personally still support the BLM movement regardless of the violence that occurred amongst the protests. The riots after Rodney King didn't invalidate what the police did to him.)
[actions of the capitol police]
Yeah, as some reporters have noted there are definitely going to be plenty of angry hearings and changes as a result of this. Several high-level resignations already. The Capitol Police's budget is not small, either - roughly $500,000,000 and with about 2,000 officers.
In my personal experience as a person-who-occasionally-lobbies-congress, I can say the officers I've encountered there seemed largely (but not entirely) decent enough but not terribly well trained. (Edit: I should probably caveat this by noting that I'm white and look/am thoroughly nonthreatening.)