Rents are rising across the city and Wedding is gentrifying heavily at the moment, it has seen up to +78% increase in rent since 2009.
The fact is, this issue is not a product of a supply issue. There is plenty of housing in Berlin, if you're willing to live in a non-trendy area and maybe take an extra stop or two on the train. In places like the Bay Area, there simply is no supply, and therefore there is a crisis.
I don't think there's a fear for displacement yet, there's quite a few plots to build up, or abandoned places that are torn down (e.g. Stattbad), and a bunch of new modern apt buildings coming up. But for now, it looks like Neukölln is the more desirable next-hip-thing.