I'm certainly interested in that Defcon talk, too... but there's probably nothing quantum about it. Most hashing algorithms are broken by finding ways to produce a collision - that is, generate some input to produce the same hash, but not necessarily the original data.
For Bitcoin, SHA256 is used as IDs to make transactions and blocks immutable. It is also used in the generation of Bitcoin addresses for P2SH transactions. So one attack on the blockchain that I can see is this:
The way that mining works is that you include a bunch of transactions into a block that pays yourself the block generation fee. The hash of all of this data (a 256-bit number) needs to be below a certain value, meaning that it needs to start with a certain number of zeros. If a hacker can generate valid data for arbitrary SHA256 hashes, then they could start with a hash that has the necessary zeros, and then work to construct block data that hashes to that value. This would likely start with a valid structure (else it would be rejected by the network), and then algorithmically-generated "garbage" data included in the block to result in the hash code.