What rights do they give for photos?
Rights can be a tricky and costly thing depending on how they have their pricing structured. It's often possible to end up spending more on getting copies of photos after the event than you spend on having the photographer at the event.
What is provided with the cost?
Similar to the previous question. Make sure you clearly understand what you are being sold in detail. Know what is included and what is extra to avoid surprises after the event.
What services have additional cost?
Often additional services are available for an extra fee. What are they and how much are they?
What equipment will you be using?
This one is a little more useful if you know a bit about camera gear, but you certainly want at least a few good lenses and at least two camera bodies. Also, note that the gear doesn't necessarily have to be the best, but they should be able to speak with confidence about their gear and have very solid knowledge of their tools. You'd likely be better off with a guy with a point and shoot that knows exactly what it can and can't do and how to get great shots with it than someone with a $20k kit that doesn't know which end to point at the subject.
What backup equipment and measures do you take?
For events backup gear is critical. It doesn't have to be as good as the main gear, but in the unlikely event that something goes wrong, they need a backup. They need at least one extra camera body, extra batteries, extra memory cards and multiple lenses that can handle the core duty for the event.
How long have you been doing this?
Knowing someone's experience is always helpful. Even if they have the best eye on the planet, experience is the only way to get good at dealing with problems on the fly without it causing a loss in quality.
Will you have additional shooters working with you?
How many photographers are you getting? This is important because even the best photographer may miss some shots and can only shoot from one angle at a time. Multiple photographers gives more options, more angles and more redundancy.
What formal background, if any, do you have in photography? If no formal background, how did you learn the field?
This is similar to how long they have been doing it. Knowing how they were trained and if it is something they just picked up on their own or if it is something they have additional study in is good to know. There are still some educated "pros" that are not as good as a really skilled person that just picked it up and started shooting and learned as they went, but it does give an idea of background.
For extra credit I'll throw in a few things you can try doing to see if the photographer is paying attention and knows their stuff.
Don't mention where the event is.
In particular, indoor vs outdoor weddings have vastly different requirements. Also, the layout of the space matters for figuring out what lenses and how many photographers would be needed to cover it effectively.
For weddings specifically, don't mention photos of getting ready.
This is an easy one for inexperienced photographers to overlook, but an experienced photographer should ask about if you want photos while getting ready the day of the wedding.
Again for weddings, Don't mention the rehearsal.
It isn't necessarily critical, but it is certainly highly beneficial for the photographer to see the space prior to the event if they have not seen it before. If they don't ask about it, ask if they've shot at that location before. It still doesn't hurt for them to know about the order of things, but knowing the space is the most critical.
See how generally helpful they are.
This isn't a guarantee that they don't know what they are doing if they don't do it, but if they have a lot of experience in the event space that you are working with, chances are good that they'll have general commentary and advise on your event in general. When you work event's you learn about more than just your own role and you know what works well and what doesn't.
If they don't volunteer information, you could try asking them more specifically for their thoughts about things related to your type of event. On the one hand they aren't your event planner, but if they know the type of event well, it shouldn't be a hard conversation for them to participate in.