Some other things, assuming for the sake of discussion that this writeup is accurate:
1. It damages the relationship of the jackboot community and the administration: the SEALs were deployed to hit Bin Laden, and were told that this would be done without fanfare. Instead, within hours, the White House and company are bragging about the whole operation. This is not how proper clandestine things are done, one imagines.
2. It damages the relationship of the jackboots in particular and the administration: having to suffer the indignity of signing what is a effectively an NDA for premeditated murder--and then watching two folks get away with breaching it because it supports the new, official story--cannot have been easy for the folks involved in the raid.
3. It damages the State department's credibility (hah) with Pakistan. We agreed that steps would be taken to reinforce the government's position with its people, and that we wouldn't implicate them--they would save face. Instead, we put up a flimsy half-baked cover story, and decide not to go with one that leads to lots of easy questions, which will never have answers that are either convenient or satisfying. Look how Gates reacted during the thing--was not happy.
4. It damages the relation of the government and its people. As seen through the FOIA requests, it's pretty obvious that several parts of the story don't really jive. So, it's obvious that there is either bad record keeping in place, or a coverup of some sort. Not in the dramatic sense, mind you, but just minor misalignments of documented reality with official story.
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The problem isn't that they had the guy whacked--it's that they perhaps did such a thoroughly and unneeded job of lying about it afterwards.
If you want to see how this sort of thing should be done, look at the Israelis.