Corrected entry: In a flashback showing the electoral map in the background, the states won by George Bush (Republican) are colored blue, while the states carried by Bill Clinton (Democrat) are colored red. It should be the other way around.
Corrected entry: In the episode "Hubris", Lily finds a quote in a letter a suspect wrote to the victim, "for wise men know well enough what monsters you make of them", which she says sounds a little like Shakespeare. She and a few other cops are later seen reading through several Shakespeare plays in an attempt to find it, but this is madness when you consider a) the sheer mass of his work and b) that she isn't even sure it's a quote from him. Much faster would have been to Google the phrase, which brings up several hundred pages identifying it as a line from Hamlet. Any experienced detective would think of this first.
Correction: True, it would have been easier, but she may not have thought of it. Besides, her stupidity is not a mistake.
Correction: The blue/red for Democrats/Republicans being consistent only started with the 2000 Presidential election. For most of the 20th Century red was used for Democrats, and blue for Republicans, if there was any consistent colour scheme at all. With the development of colour TV, some networks alternated the colour scheme with each election, or had their own preferred choice, such as using blue for the incumbent party. The drawn-out nature of the 2000 election meant that the electoral map was referenced for much longer than normal, and networks standardised for simplicity, and the current scheme stuck. There was apparently no particular reason for the specific associations, and the parties themselves had no official colours.