From WSJ.com: Should You Pay Your Mortgage With Plastic? - WSJ.com
For 0% offer, usually comes with huge (4-5%) transaction fees. And I have not heard any cashback or reward points for those BTs. Navy FCU is the only recent one with no-fee BTs (and it is a promotional offer once a year).
This is something profitable: Use a reward/CB credit card to pay mortgage/tax. (1) find out whether it indeed comes with CB, many do not. Put your cash advance limit to zero and test out first. (2) figure out the gain beforehand. Say it is a 5% CB (for everything) card, and the fee with credit card is (usually) 2-2.5%. Then there is a worthwhile gain. But there is rarely a 5% (for everything) card offer. If the card only gives back 2%, then it is certainly not worthwhile.
As a footnote, there are ways to pay tax with credit card (usually 2% fee). But to pay mortgage with credit card, there is relatively fewer choices (i.e., a few website services only).
In sum, use 0% offer and invest on other vehicles (e.g., RCAs); not in mortgage/tax payment. Use only 5% CB card (if one has one) to pay tax/mortgage with fees.