In b6, String no longer magically bridges to NSString. String is not a class; it’s a struct. You need to do the bridging by hand:
dict["key"] = "value" as AnyObject
The fact that is still seems to be bridging is likely a bug and should be reported.
It goes without saying that [String: AnyObject] and [String: Any] should be used as little as possible in your code.
(Make sure to follow the link Hamish provides in the comments below.)