So let's see.. get a bunch of people together who are overly focused on it's study, who make it their life and are, for the most part mystical or untrustworthy and then give them toys to play with.. now do this under one roof. Oh yeah, there's gonna be mishaps!
As for the arena, it never made sense to me. In vivec they get a whole giant building, but in the imperial city it's a section? How exactly do they bring the creatures in? Where is the holding area? And who really makes the decisions? For that matter, why can I only ever see one team? Why are there no "freelance" fighters signing up or hanging around like there would be in a real one? Even vivec has a few walking around the compound and they don't have the kind of fights the imperials do!
The whole place needs a rehaul frankly, and if they have to drag dangerous sorts in to the place for people's viewing pleasure, it seems odd to have it where it was without a lot of explaining. Even in rome most of these places were, although well used and well liked, not in the center of town. Still you will want to keep in mind that the denizens of the city would want easy access to the place, and the guards would want it near the city were they could keep an eye on it and call for help if needed.. they certainly would not want it on the outskirts though.. many fighters, especially freelancers, are unsavory sorts that would require careful attention when they weren't in the main areas of arena.
So prolly have several entrances would be feasible. Like say, a main entrance that would be inside the city, providing easy access to the locals and would be on a guard's patrol route and one a little bit out of the way. The one in the city could be a faster way to viewing and social areas, with a gladiator processing area not far away and the entrance that is a little more out of the way could be closer to the areas the fighters might use, and be closer to the area they use to process the creatures and stuff like that. (maybe have the creature area led far outside town through underground tunnels)
Underground tunnels. Even the Roman's used them. They allow you to bring in fighters and material without taking surface routes.