The order Mononegavirales includes three virus families that replicate in the cytoplasm: the Paramyxoviridae, composed of two subfamilies, the Paramyxovirinae and Pneumovirinae, the Rhabdoviridae and the Filoviridae. These viruses, also called non-segmented negative-strand RNA viruses (NNV), contain five to ten tandemly linked genes, which are separated by conserved junctional sequences that act as mRNA start and poly(A)/stop sites. For the NNV, downstream mRNA synthesis depends on termination of the upstream mRNA, and all NNV RNA-dependent RNA polymerases reiteratively copy ("stutter" on) a short run of template uridylates during transcription to polyadenylate and terminate their mRNAs. The RNA-dependent RNA polymerase of a subset of the NNV, all members of the Paramyxovirinae, also stutter in a very controlled fashion to edit their phosphoprotein gene mRNA, and Ebola virus, a filovirus, carries out a related process on its glycoprotein mRNA. Remarkably, all viruses that edit their phosphoprotein mRNA are also governed by the "rule of six", i.e. their genomes must be of polyhexameric length (6n+0) to replicate efficiently. Why these two seemingly unrelated processes are so tightly linked in the Paramyxovirinae has been an enigma. This paper will review what is presently known about these two processes that are unique to viruses of this subfamily, and will discuss whether this enigmatic linkage could be due to the phenomenon of RNA virus error catastrophe.