Can there be appeal? Judge abd court make mistakes …

There's no need to appeal yet. With "punishment order" they probably refer to a german "Strafbefehl" which isn't a full sentence but a simplified system to avoid trials which only requires a bit more than probable cause.

They can now object to it, then there will be a full trial. If they loose there, then they can appeal.

HN ranking history for this story: https://hnrankings.info/37244534/

Context?

american satirist found out that there are other sovereign nations with their ow laws.

May I point out a slippery slope is that sort of argumentation? American people have some basic rights protected by constitution. If these can be circumvented by shipping their trials to another country, then what's the point?

there's this thing called extradition thingy. i guess there's no point in it, then.

He lives in Germany

Is this like getting a parking ticket from a private company? What if he just tells them where to go?

He lives in Germany as a permanent resident. So he can either appeal, pay the fine, or move back to the US (plane tickets alone would cost more than the fine, let alone the cost and disruption of moving a family).

If he lived in the US, he could likely just ignore the ruling. This would clearly be 1A protected speech in the US, so even if Germany pursued it, they would be politely told to screw off. It would probably be a bad idea to return to Germany though.

Summary: The German court accused him of "disseminating propaganda, the contents of which are intended to further the aims of a former National Socialist organization."

The point of TFA and his defense is that he was "using the negative connotations of Nazism to criticize a currently serving government official."