What are pros and cons of Tendermint? The writer describes it as a "solution to the blockchain consensus problem that does not require mining."

The white paper is viewable here:
http://tendermint.com/docs/tendermint_v04.pdf

I don't mean what are the pros and cons in relation to Bitcoin specifically, since I don't believe Bitcoin is likely to take it up. I am thinking more of the possibility of a popular altcoin like Dogecoin adopting it, or perhaps an smaller altcoin e.g. Reddcoin.
I'm the author of the paper.

PoW mining may be wasteful, but it's a great distribution mechanism.  Coins and other applications that use Tendermint might want to tack on a distribution mechanism that tapers off over time.  I'm also exploring alternative distribution algorithms that don't require PoW, but for now I'm busy implementing core Tendermint.

Dogecoin could adopt it with a hardfork.  Alternatively, one could take Dogecoin's transaction data and create a new coin using Tendermint's consensus protocol.  The biggest problem with this is that exchanges and wallet services may benefit unfairly.