c) The Ministry generally seems to be portrayed as fairly competent...

But I'm reminded of this exchange in Chapter 61:

Madam Bones's voice continued. "We brought in Arthur Weasley from Misuse of Muggle Artifacts—he knows more about Muggle artifacts than any wizard alive—and gave him the descriptions from the Aurors on the scene, and he cracked it. It was a Muggle artifact called a rocker, and they call it that because you'd have to be off your rocker to ride one. Just six years ago one of their rockers blew up, killed hundreds of Muggles in a flash and almost set fire to the Moon. Weasley says that rockers use a special kind of science called opposite reaction, so the plan is to develop a jinx which will prevent that science from working around Azkaban."

And there's the fact that interrogation under Veritaserum seems to constitute the entirety of serious criminal investigations.