The case in which Booth and Aubrey arrested Alex Rockwell happened less than a year prior. There's no possible way he could have already been convicted and be nearing his execution date because even if his trial was held in a timely manner, convicts spend years on death row before the execution actually takes place.
Where were the murders supposed to have taken place? Washington, D.C. abolished the death penalty in 1981.
At 53:32 the intern with the last name Fuentes is pointing out something to Dr Brennan. He states "it is new". Dr Brennan says "what is it Dr Fuentes". Dr Brennan never refers to an intern as Doctor, she always refers to them as Mr. or Miss.
Dr. Fuentes finished his education and received a doctorate in Cuba before moving to the United States. His degree is not recognized in the U.S. so he is redoing his studies. Dr. Brennan recognizes that he is a forensic anthropologist who has already gotten a doctorate, so this is why she calls him doctor and the other interns Mr. or Miss.
Hodgins says that he's been going over every piece of his evidence, "every particulate, every fungi." Hodgins should know that "fungi" is the plural form of "fungus."