What do you like best?
It's owned by Google! Of course you gotta go with the powerhouse. My colleague used to always say, "You don't get fired for choosing DFP". In all seriousness, I've used several ad servers and DFP does actually have a nice UI. It's mostly well organized and fairly simple to use.
What do you dislike?
It can be very clunky at times, but most if not all ad server are; which is understandable due to the frequent updates and near real time performance statistics. If you are one of the unlucky ones and work in a faced paced, high stress environment, it will drive you crazy. If you are lucky and work in a somewhat relaxed environment, you can take care of other things while DFP processes.
Recommendations to others considering the product
Go for it. Almost everyone uses DFP so it's easy to find talent and collaborate with others. Their support team also does a good job responding to issues/inquiries.
What business problems are you solving with the product? What benefits have you realized?
Ad serving of course. Selling ads, trafficking ads, keeping track of ads and making all the money. DFP has almost everything you need.