One of the pieces of advice in this podcast is to basically just listen for the first week, possibly for the first month, that any changes you make this early will spend your political capital and leave you with nothing for the next change you want to make.
Seems very reasonable, but here's my question/problem. What if your entire purpose in being put into the new position is to "fix it"? The organization is broken and you need to go in and start making almost immediate changes. Possibly you can wait one week, but anything more than that and you lose that same political capital with the management that is putting you in to "fix it".
I get that it will cost. You will lose with the direct reports, but can you afford not to? How do you balance this out?