Organization is Key to Turn-Around Potential
The example in the article states the project has to get done, but that doesn't mean there's an organization capable of doing it. So, I'd like to add that to the list.
For starters, there has to be top-down support, someone with authority has to be supporting the project and in a reasonable way. Anyone considering taking a turn-around PM job, first find your top-down authority, then you yourself will have to determine "reasonable", because of all the myriads of possibilities that make a project impossible. For example, one exec asking me to take on a turn-around had another manager doing v2 of the same product, WHILE V1 DIDN'T EVEN EXIST YET! The v1 team was morale was in the gutter, the v2 team was, too, knowing their mgr was really a snake in the grass (and siphoning off all the specs/docs/code from the v1 team to figure out which way is up), and the exec over it all was totally clueless, but willing to approve funds, staff, etc. "to just get this done ASAP!".
The list could go on as to all the possibilities; experience has taught me by the time a project is in turn-around mode, the odds are the real problem is not getting fixed when they're looking for a turn-around project mgr.