UPDATE!
OK, so everything turned out OK dealing w/the water streaming into our condo. This morning there were these three lines in our ceiling where you can tell it is damp. Other than that all the water spots and the rings around the air vent and the small light had dried. We got a hold of the Homeowner's association and they sent two people out here to look to see if there is any damage. The good news is that there isn't, all I have to let it do is dry and they will come back out in a few days and touch it up. They only way they would have had to tear up the ceiling is if the water hadn't drained out and it was trapped in the ceiling. So the next thing was trying to figure out how exactly this happened. At first after my neighbor called a plumber we thought that the drain pipe was clogging up and it pushed all the water back and flooded his kitchen/laundry room. That wasn't the case though. We went up to his condo and turned on the washer, and instead of the water staying in the tub of the washer, it all started running out the bottom, so that's how it ended up leaking. The strange thing was though that he had used his new washer for a week or two before this happened and it only started doing it after he re-rinsed some shirts last night. So anyways, the guys that came out to look at it didn't understand why water didn't come out in our laundry room and why it didn't come out the other main light in the kitchen and also out the two sprinklers too as well as the vent and the small light. The only thing they could think of was that the building was built on a slant and that's why it only came out those two places. I guess a semi-slanted building is a good thing in this case. Oh well, so we don't have to pay anything and we don't have to tear up the wall or the ceiling, thank god. And our neighbor is really super nice and we were able to resolve everything and be nice about it. So all I have to do now is keep an eye on the ceiling as it dries and make sure nothing else happens.