Pros
I worked at the Tokyo, Japan branch of the Goehte Institut in 2018. The local staff (Ortskräfte) are very nice and competent people. They worked there for many years and have much knowledge to share. The local staff consists mostly of Japanese, who speak German rather fluently.
Cons
The management (Gesandte) system is extremely flawed. Unlike the local staff who are permanent, the management staff rotates about every 4 years. The problem is, that 4 years is rather short, considering that the staff has to acclimate to the new country and understand how the different culture works. Gesandte usually won't even try to learn the language of the country they are stationed in, which also causes them to not open up to foreign cultures at all. They live in their little bubble (the workplace where everyone speaks German), but have no social life outside of work, so they expect the local staff to also sacrifice their private time and energy for work. (In general some of the Gesandte treat the Goethe institute like a religion instead of a workplace...) The self-inflicted social isolation of the Gesandte is a big problem and you can tell, that some of them developed psychological disorders over their career of moving from one country to another every 4 years without having a private life in any of them. I also saw blatant cases of racism, like openly yelling at local staff during meetings, if they have a question or there is a German word they don't understand. "Are you stupid or what?!", "I won't say this twice so make sure you understand it the first time!" and such... Extremely toxic. Saw local staff shivering with fear and nearly crying during meetings on several occasions. HR exists only formally, but in the case of the institute I was working in, there was just only one HR guy and he was too busy licking the boots of the top management as to stop any of the dubious practices going on. The general racist "Germany is superior" thinking goes so far, that the management tries to evade the local laws of that country, justifying it that "that's how it works in Germany!". If local staff tries to explain why certain things cannot be done like in Germany in this country, the management gets angry and says "We are a German institution! Stop siding with the Japanese! We do it the German way!" If you plan on joining as an intern, don't. I met about 7 interns over my time there and without exceptions they all regretted spending so much money to come to Japan just to be exploited by the Goethe Institut.