Judd Hirsch is an astro-physicist and can actually do the math Charlie does on the show. He caught the acting bug in school and chose that over physics. See more...
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Factual error: Season 1, Episode 10, "Dirty Bomb": The opening figures refer to "500g of Nuclear Material." These are the wrong units to determine the hazard level in a radiological sample. The "Curie content" describes, roughly, how much radiation will be given off, and is not tied directly to the sample's mass. 500g of Cesium-137 (the isotope being discussed in the episode) could well be less radioactive than 1g of a different isotope.
Continuity: When Charlie is in his office talking to Larry, while going over the potential killers and victims, he writes the word "Killers" on the board and circles it. Then, when Charlie notices that Larry has left and says "gone", the writing is different. The 'k' is wider, and most noticeably, the left side of the circle is gone, and the loop in his 's' disappears. Once Charlie goes back to working, the word changes back to how it was originally written.