Many riders report that they have unheard of numbers of flats when it rains -- three flats in four rainy days, for example. This is unfortunate, as riding in the rain is nice for the cool air, lack of traffic, and low rolling resistance, but there is a reason for all the flat tires.
First, riders can usually spot glass ond gravel to steer around it. When the entire road is shiny, this becomes really difficult. The fact that rain can wash debris from the center of the road to the margins, where many cyclists ride, complicates the problem.
The main problem is that when rubber is wet, it becomes much easier to cut. One author noted that he had great difficulty carving out the rubber to place a cleat in a new pair of cycling shoes. When he wet the knife, the rubber became quite easy to cut and the task was soon finished. It may be the case that the water lubricates the penetration of a sharp object through rubber. As a result, a much less sharp stone or a smaller chunk of glass can cause a puncture than when the tire is dry.
I've only ever had one puncture (plus two pinch flats from underinflation and a blowout from an impact), but I generally only train on nice days. It's amazing how durable a tubular racing tire can be, from driving over broken beer bottles and endless kilometers of gravel roads. However, it would be wise to be extra cautious in the rain, and stick to parts of the road that you know to be free of debris.