When Jennifer is in a cell and Olivia is talking to her, Jennifer is having a break down and doesn't remember killing Elsa, however when Olivia asks her how long she had been awake when she killed Elsa, Jennifer responded immediately as though she hadn't forgotten.
At 36:23 Detective Benson asked Jennifer how long she had been awake before killing Elsa and Jennifer immediately replied with "six days." However, Jennifer stated just moments before that she didn't even remember killing Elsa, so she shouldn't have been able to come up with that answer so quickly.
The M.E. talks about analyzing oxygen isotopes from the victim's hair. However, sulphur isotopes are the most common in keratin, from which hair is made of.
Albert Einstein never actually took a IQ test, mainly because his academic years were before the IQ test existed.
When Jennifer appears in court she is wearing an orange prison jumpsuit, which is something a defense attorney would never let a client do, especially a pretty young girl, the attorney would want her to have her hair fixed nicely, wear makeup and a nice dress or skirt. Having the defendant wear prison issue clothing in court can bias the jury, and even the judge, against the defendant, if they are wearing prison clothing it makes them think of the defendant as a prisoner and not a person. That is why the law allows for a defendant to change into normal clothing for all court appearances, including motion hearings, not just trial; and most judges will insist that the defendant be given the option to change clothing in order to avoid any appearance of impropriety.