Filming or taking pictures in itself is not a problem and perfectly legal. Go film all you want. You're just not allowed to publish those pictures. So if you see a suspicious act, take your pic, hand it to the police and let them deal with it.

You can film the police and film public figures all you want, as long as they're acting in their public capacity. You're allowed to film Angela Merkel doing her state visit, going to the beach with Barack Obama and later publish that clip. You're not allowed to film her naked in her private backyard.

The border between the two is sometimes hard to determine, so there are some lawsuits about that, but all in all it's pretty clear.