This is our fourth paper in our five paper series describing our national study of general education astronomy students' conceptual and reasoning difficulties with cosmology. While previous papers in this series focused on the processes by which we collected and quantitatively analyzed our data, this paper presents the most common pre-instruction conceptual and reasoning difficulties identified from our qualitative analysis of students' written responses. We discuss students' naive ideas about the expansion and evolution of the universe, the Big Bang, interpreting Hubble plots, and the evidence for dark matter in spiral galaxies. (Contains 10 figures.) [For Part III, see EJ971055.]