[Note: CROWLEY-GATE(S) I is here. CROWLEY-GATES(S) II is here.]
Though frustration is understandable on the administration's part, Obama likely should have said nothing more. But if not, he needed to back up what he said, while very clearly changing the "Cambridge police acted stupidly" part of the comment -- which was poor wording on his part, overly pejorative, far too subjective, and unnecessarily and accidentally appeared to impugn the department, when what Obama was referring to was the officer involved. Short, simple, to the point. Case closed. He should not have involved himself directly in the matter further, by calling the two principals involved (Professor Gates and Sergeant Crowley).
Instead, the President, in addition to calling both Gates and Crowley, made another lengthy statement that helps legitimize this as a bigger (and more national) issue than it really is. By so doing -- although his statement was substantive -- it in some way also plays into the media pack rat appearance and sound bite over substance scandal machine, that along with Obama (who did so unintentionally), helped create this issue out of a relative non issue to begin with.
[Update: The President also plays along by trying to patch up something that does not need patching up. See CROWLEY-GATE IV, here.]