I receive messages like STATS: dropped 71. What does that mean?

It means that 71 log lines are dropped since the last STATS, because somewhere wasn't enough resource to receive them. Maybe the other end listening on tcp closed? Or there is a fifo destination with no listening process at the other end? Note that in case of udp you will not even notice that you have lost some log lines. Sometimes these messages generated because you have an xconsole (or other pipe) destination, but have no one to listen on it.