How does DNA replication differ from the manufacture of an RNA molecule?

One of the biggest differences, aside from the fact that different enzymes and different precursors (ribonucleotide vs. deoxyribonucleotides) is "proofreading" ability. That is, DNA synthesizing enzymes must replicate DNA faithfully, and have a "proofreading" function that removes mistakes made during synthesis (e.g., substituting Guanosine for Adenine, for example). RNAs are typically not hereditary materials, and RNA polymerizing enzymes typically do not have the proof reading function of DNA polymnerizing enzymes. Thus, RNA molecules tend to be made with more replication "mistakes" than DNA. This really is no big deal. Say a thousand mRNAs are made from a single DNA; who cares if one has a mistake. Most mistakes would result in a protein that does not function. But, there would still be 999 mRNAs around to make that same protein.