Joey D’Antoni points out a potential big performance problem with clustered columnstore indexes:
In the last year or so, with a large customer who makes fairly heavy use of this pattern, I’ve noticed another concern. Sometimes, and I can’t figure out what exactly triggers it, the execution plan generated, will do a seek against the nonclustered index and then do a key lookup against the columnstore as seen below. This is bad for two reasons–first the key lookup is super expensive, and generally columnstores are very large, secondly this key lookup is in row execution mode rather than batch and drops the rest of the execution plan into row mode, thus slowing the query down even further.
Joey also has a UserVoice item as well, so check it out.