Will the 3G SIM card from my original 2010 iPad work in the new 2012 iPad, or will I need a new SIM card?
This will depend largely on your carrier. If they're offering 4G/LTE service with the iPad 3, you may need a new SIM card. If they're not offering that service in your area, it shouldn't matter if you have a new SIM card or not. Your best bet is to ask your carrier.