- English: verbing and nouning. All languages have ways of introducing new words, but only in English I've seen it accepted as something anyone can casually do in a throwaway manner. Have a noun but want to talk about the (contextually) default action related to the noun? No big deal, just stick an "-ing" or "-ed" to its end and carry on. I adore this feature.
- German: word concatenation you mention, it's a killer feature. And then there's the peculiar grammar that puts the most important verb at the very end of a sentence, giving you stuff like "Gegen die hohen Preise für Gas, Strom und Treibstoff will die Regierung etwas machen", meaning "The government wants to do something about the high prices for gas, electricity and fuel", but structured as "<tone> <stuff> <blah> <blah> <subject> <stuff> do something". So not only you need to listen to the end of a sentence to know what it's about, but you can actually zone out a bit early on, catch the last few words, and still recover the meaning. I'm sure one could write an interesting signal processing take on this.
(If anyone knows examples of such unique/special "skills" for other languages, I'd love to hear about them!)