The Correspondents Dinner has a tradition of self-deprecating humor. The president roasts himself; makes fun of his own mistakes or foibles.
The question is where the cost of the mistake is. Self-deprecation is appropriate when the result of the mistake is your own humiliation. It means you have a sense of humor about it, enough to show that you are bigger than the humiliation.
The failure to find WMD had plenty of cost. Bush and his handlers evidently believed that the only cost was that it made him look silly; that it was a hit on his credibility. Self-deprecation is about overcoming that momentary lack of credibility. It's incredible that they thought that was the only issue, and that making fun of it was enough to overcome it.
It proves that they saw the other costs of the failure - including deaths of soldiers - as irrelevant. In fact, it's worse - it proves that the other costs of the failure didn't even register to them. Because it wasn't just about them believing they were irrelevant - it was that they didn't believe they were even worth acknowledging to the entire media.
Republicans are completely incapable of self-deprecation, because it involves actually acknowledging a mistake or vulnerability. Bush's joke wasn't an admission of vulnerability. It was a crass declaration that the failure to find WMD didn't even matter to him. In a way, it was the opposite of self-deprecation, because rather than admitting humility, it exposed arrogance.
I think the ad does a good job of exposing that arrogance.