The available grip you have is greatly diminished. When cornering, you'll want to get your weight a bit more over the front wheel to avoid it sliding out (happens easier than you'd think, depending on the type of asphalt).

If in doubt of traction, use the rear brake. You can lock up the rear with no problems. The front however, is bad.

New blacktop, especially in parking lots, is very, very slick when wet. The fresh tar mixes with the water, and is basically like a very thin oil slick. You won't know that until you try to turn, and wind up on the ground.

Hydroplaning isn't an issue, as your speeds probably aren't high enough, and the tires are very thin. Puddles should be viewed with caution, however, because you don't know how deep they are.

The little lip between the sidewalk and the road will mess you up if you try to cross it with a shallow angle of attack. Your wheels will just slip off of that 1" rise, and you'll be sliding across a busy road (yes, that happened to me, I broke a collar bone and messed up my rotator cuff). So if you need to cross that gap, either bunny hop onto the higher/lower side, or take it with a high attack angle, like 35' or so.

Drop your tire pressure 25% off whatever you normally run. You won't notice the speed cut due to the rain, and it will give you a lot more traction and feel.