Someone (here: http://www.fatwallet.com/forums/hot-deals/550192/m7500010/#m7500... asked where to find the serial number on a Panasonic shaver. I too looked high and low for this elusive creature and saw that many others on the net have as well. From what I was able to gather (and I post this here in the hopes that it will help others in the future), the serial number...is actually the model number! So if you go to Panasonic's registration page (https://secure2.prodregister.com/pnaportal/welcome.aspx), simply put in your model number. All they care about is if you have a receipt for your purchase and that the model number on it matches what you purchased.
Like I said, I hope this helps others in the future!