Twitter, after making headlines for enabling encryption with perfect forward secrecy, has apparently abandoned the next stage of the project, which is to encrypt private messages within the service.
Without a reasonable explanation for this action, there is a lot of speculation as to why they would abandon a project that Twitter had already invested significant resources into. It could be a legal issue operating behind closed doors, it could be that they are overhauling the messaging system (again) and do not want to devote resources to message encryption until the overhaul is complete, or it could be technical hurdles.
The fact that they remain silent on the topic is troubling. One thing we have learned is that when a gag order is issued, companies remain silent about their actions, and aren't allowed to even acknowledge that any such order exists. Until a real explanation is given by Twitter it looks suspicious for them to drop a project that they are obviously passionate about, and had already been under way.
For now, we recommend that you do not use Twitter for any private/sensitive information of any kind.