I would think choosing a wedding photographer would be very difficult. You are hiring someone to capture your special day. All the memories. Every detail that makes that day special.
I would choose someone who has experience shooting weddings, can demonstrate varied styles of photography--photojournalism as well as candids. When looking at their work I'd look for sensuality, a certain softness in the pictures. Also, how well they shoot faces -- it isn't just the action shot that's important, if you are able to see peoples' faces in the pictures, that shows the photographer made a connection. I'd choose a photographer that shot in color as well as black and white. Someone that would make me feel comfortable. Someone that can support that by not making me worry about the smaller, less important pictures like the cake. A photographer who would feel the freedom or sense that if they see something cool going on someplace, they can capture it. Magic is better to shoot for than coverage. Someone that would go for quality, not just quantity.
I'm sure there are more things I would look for if I put more thought into it.