Factual error: There are some majors problems with the "jumper's" crime scene. The girlfriend bashes the boyfriend on the back of his head. He bleeds out all over the balcony (she cleans up the blood with towels) but the body leaves absolutely no blood behind on the carpet (It's white\off white so blood would stain badly). She drags his body across the carpet and carpet fibers get stuck in his watchband by the adjustment knob. Dragging a body across the carpet would snag fibers on the opposite side. The CSI crew experiment and conclude the boyfriend was pushed. The blow to the head killed him instantly (coroner's report): therefore, the girlfriend would have dumped the body. Dumping a dead body over a rail would provide a different trajectory than pushing a live person and would not have matched their experiments. Finally, the boyfriend is fairly muscular and heavy. The girlfriend is petite. It would be an extremely difficult task to stand a lifeless body up at the balcony rail and flip him over. (If she could have lifted him up and over the rail, she should have been able to carry him to the balcony instead of dragging him.)
Factual error: Grissom and Catherine are looking through a microscope and discussing a microscopic specimen (heart of frozen body). In reality they would not see anything as all microscope objectives are missing on this instrument (the microscope nose-piece is totally empty.).
Factual error: The show falls into the Hollywood myth on polygraphs. Jesse is given a polygraph test after pleading guilty to the 4 murders. He answers all questions, except the last one, honestly. The 4 traces on the polygraph show no real movement on these questions. On the final question, Jesse lies and all 4 traces spike. If polygraphs actually did that, they would be admissible in court. But the reality is, it is the opinion of a highly trained operator that decides if there is a lie. The average person could not look at a polygraph results and point out a lie. There is no huge, visible spike. The producers could have replaced the 4 traces with a red\green light: Green is an honest answer and red a lie.
Factual error: When Gris and Teri are looking at the bones that were found in the desert and discussing an electric saw, Teri is talking about the medial condyle of the femur but the bone they are looking at is the tibia (seen by the flatness of the tibial plateau - the femoral condyles are much more rounded, and the triangular shape of the shaft of the bone). It makes no difference to the story but having gone to the lengths to get the scaphoid and cuneform in the right place, it would have been nice not to get two major bones, that look completely different, mixed up.