The only significant side effect, in general anyway, of taking expired birth control pills is that they will not work. There may be the odd case that gives you other minor symptoms, although it is unlikely that you will have any serious side effects. With that in mind however I would mention it to your doctor and if you do notice anything out of the ordinary you should visit your doctor right away.
Expiry dates are usually used in reference to when the product will lose its efficiency. I would like to think that most medications would not significantly harm anyone if they are expired but I would never suggest to anyone that they take expired medications for more reasons than that it just may not work.