(The following is not spoiler)
I wouldn't call MItsuhiko "idiot" here. He just doesn't know what he's doing is dangerous. Even though secretly filming people is not really a right thing to do, but he has no bad intention whatsoever. There is no wrong in searching for the person who saved your life and show your gratitude. Seriously, if it was me, I would probably do the same thing, and I'm sure many people in real life would do that too. At least the DB are still better than those ungrateful people we meet everyday.
But the point is, MItsuhiko is not stupid, in fact, he knows how to make a cellphone useful for investigations, this point alone already proved that he's much more superior than Ayumi, Genta, 90% of the "general children" in DC, and most of us real people of that age. He knows when is important to film a video. In the Takagi kidnapping case, had it not been for the footage that he recorded, Takagi would be in the graveyard right now. Actually, nobody would think of filming an extra footage because it wasn't really necessary at the time, but he still did it just in case, and that decision saved a person's life. In this case, he is aware that just basing on the impressions that the woman gave them doesn't help finding out who she is, so he immediately filmed a video. That way, not only that they don't have to remember her face, her clothing, her voice; but it's more convenient for them when seeking help from other people (this time, Kogoro). Actually, he's aware that using their ability alone cannot locate the woman, so he filmed it especially for Kogoro (unlike Conan, who most of the times thinks he can do everything by himself). Furthermore, his filming skill is good enough for the target (Sherry) not being able to notice it, this may be useful in future cases, as he can film suspects/criminals without them knowing.
Anyway, I just want to say that we shouldn't always look at the negative side of the DB, just because the damage they bring this time is too big (again they do not know that it's dangerous). They can do good too (although there've been multiple times where they almost get themselves killed because of their annoyance). Also there is no guarantee that Mitsuhiko is not in cahoot with Bourbon or the BO in genenal....