Pros
Good training program for entry level people. Quite a few smart people around. Great offices to work in - very attractive, good location, communal kitchen, lecture theatres etc. Office in general feels quite busy & bustling. Lots of perks like free theatre/exhibition tickets, events etc. Good amount of responsiblity from early on. Good pay. Good name to have on the CV.
Cons
Lots of the codebase is pretty antiquated - Fortran code, old 1000 line C functions from the 1980s etc. Lots of proprietary stuff you have to learn that isn't transferrable, so you run the risk of getting a bit institutionalised. Also, Bloomberg often unnecssarily has it's own little version of something (file I/O libraries etc). Senior management have their head in the clouds & are fairly political - many have been since the dawn of time and have an outdated view of how the company works, and they will push through initiatives that they have 'sold' to their superiors even if they just don't make sense at ground level. One of those companies (and there are many) that sell themselves to applicants as having a 'flat' structure, when what this actually means is that hardly anyone ever gets moved up. There is also lots of bureaucracy and a culture of micro-management - every working hour must be ticketed, accounted for etc.