The general consensus in the german legal system is that a dashcam that records on loop is not allowed; you basically film people without their consent and with the intent to distribute to third parties (the police) for no good reason (the possibility of a crash).

On the other hand, what is permitted is dashcams with shock sensors and trigger buttons. The shock sensor gives you a good reason (very high probability of a crash).

Using the trigger button is okay if either there was a crash (or something illegal) or if you mask out any identifiable details about the car and person involved afterwards.

Generally, recording public spaces is illegal, if you setup a security camera on your property, you have to make sure it's not filming outside your property in an unreasonable manner (you may be allowed to film the sidewalk, for instance, if you suspect someone is salting your garden out of revenge, but only until you have proof and then you have to make sure to delete all non-essential footage).

Privacy in public space is an important right that doesn't exist in the US.

It is a weird one in Germany. Generally you can record everything because of a law called Panoramafreiheit, however once you start to have discernible individuals on your photograph/video you need their consent, because individuals own the Bildrecht (”image rights”) to themselves, while you as the creator own the Urheberrecht (”creator rights”). And it needs both for a image to be taken legally.

So you get their written consent, ask them if it is okay or take the risk that they will e.g. see themselves in your movie and force you to take it down. This fits with the general feeling that filming another person without asking is seen as extremely rude.

The key here is that people need to be recognizable, so pictures of crowds usually don’t count.

Certain architects can also forbid circulation of photographed versions of their building if it is central subject of the photograph — but I only know of one such thing.

Note that this all was enshrined in law way before GDPR.

Unless you stick your camera into other people’s faces without asking or plan to distribute your images on a bigger scale you will probably manage without ever hearing about these laws.

>So, I assume that recording in public spaces is illegal in general and they make a specific exception to allow dash cams on the conditions mentioned?

The act of recording isn't the problem but the retention of the data records. If you have no need to keep a recording of a day's video for any purposes, then that falls under the provisions of likely being exploited data (e.g.: being used to build a profile of a person's travels throughout the day, week, year, etc.).

In the sense of the allowances, it's about balancing the need of the data's use (e.g.: in car accidents) versus the privacy impacts to other individuals (e.g.: you post your dashcam footage to YouTube and don't obfuscate faces or license plates).

An example of this, pre-GDPR, was when Google was forced to obfuscate faces and license plates in Google Maps for Street View.