At the beginning of the game, the Mayor will ask you to 'Fire All Black Officers', but you'll see that one of your best officers is black (he'll have around 800-1200 experience). Obviously you don't want to fire him, or any of your other officers. So you can ignore this request if you want to - I did. There isn't any major repercussions for not following this order, except for City Hall not liking you for a bit.

You don't always have to send officers to City Hall's requests. Occasionaly during the day, City Hall will ask for a number of officers to do something for the Mayor. This can range from judging a Hot-Dog eating competition to protecting the Mayor whilst he goes for a walk. Note that if you answer this and send the (will most likely be 2) officers, you will lose those officers for that day and cannot use them until their next shift.

The Mayor is a ******, but he's your boss. Every 5 days, you'll be able to request something from city hall, these include: A pay rise, improvements to your SWAT Team, An additional officer slot, and an additional detective slot. If you have a poor reputation with City Hall, then they will deny these requests every time (and occasionally cut your budget, meaning you'll have to fire officers - sometimes illegaly). But if you keep a good standing with the Mayor, you'll be able to have one or more requests accepted at the same time. By the mid game I was able to request one of everything and got accepted every time as long as I kept a great standing with the Mayor.