Q: How do you know if you have a iPad mini with retina display? Can I use the serial number somewhere to double check?

For information on your iPad (model, date of production, etc) then enter your serial number at this site. Information, based on the serial number, will be shown.  http://www.chipmunk.nl/klantenservice/applemodel.html

Identifying iPad models

http://support.apple.com/kb/HT5452?viewlocale=en_US&locale=en_US

 Cheers, Tom

You can enter your serial number here:

https://selfsolve.apple.com/agreementWarrantyDynamic.do

And it will tell you exactly what it is you have.