Character mistake: Horatio writes the symbols for sulfuric acid, H2SO4, on a clear board. Both numbers should be subscripts but he writes the 4 as a coefficient (which precedes the name of the acid but he writes it after), suggesting a lack of basic chemistry knowledge.
Episode #4.1 - S4-E1
Character mistake: Ruth requests a search of London streets with the name "Achilles" in them. A list of streets appears on a computer screen, but when one of them is selected, it is spelled "Achillies."