Transmission of cellular identity relies on the faithful transfer of information from the mother to the daughter cell. This process includes accurate replication of the DNA, but also the correct propagation of regulatory programs responsible for cellular identity. Errors in DNA replication (mutations) and protein conformation (prions) can trigger stable phenotypic changes and cause human disease, yet the ability of transient transcriptional errors to produce heritable phenotypic change ('epimutations') remains an open question. Here, we demonstrate that transcriptional errors made specifically in the mRNA encoding a transcription factor can promote heritable phenotypic change by reprogramming a transcriptional network, without altering DNA. We have harnessed the classical bistable switch in the lac operon, a memory-module, to capture the consequences of transient transcription errors in living Escherichia coli cells. We engineered an error-prone transcription sequence (A9 run) in the gene encoding the lac repressor and show that this 'slippery' sequence directly increases epigenetic switching, not mutation in the cell population. Therefore, one altered transcript within a multi-generational series of many error-free transcripts can cause long-term phenotypic consequences. Thus, like DNA mutations, transcriptional epimutations can instigate heritable changes that increase phenotypic diversity, which drives both evolution and disease.