The flashing alarm clock in the victim's apartment shows the time as 4:47. This time appears on this clock at both the beginning and end of the episode. Even when a clock has been unplugged and plugged back in (making it flash), the time will still advance. The chance of the time being the same in both instances is 720:1, unless we're able to see the PM indicator, in which it's 1440:1.
The cockroaches seen crawling on the floor when Hodgins arrives at the apartment are not the type of cockroaches found in DC. The type seen is the Madagascan hissing cockroach (Gromphadorhina portentosa). The types found in DC are the American Cockroach and the Smokeybrown Cockroach, both of which have clearly visible wings on them unlike the ones seen in the show.
After Booth finds the hockey puck among the victim's belongings that fell into the apartment below, he says that he's going to keep it. All items are potentially evidence in the case and should be treated accordingly. Additionally once the case is resolved, the victim's possessions belong to his estate and aren't up for grabs by anyone who isn't connected to that estate.
Hodgins says that he found traces of "uranium-235", which came from the glazing on a garden gnome. While small amounts of uranium were used in the past to add colors to ceramic glaze, naturally-occurring uranium is over 99% uranium-238. The only way to produce a significant amount of uranium-235 is by artificial enrichment.
Booth tells Sweets that the soldier he is staring at is, "a full-bird colonel in the Rangers." Rangers no longer wear black berets. When the army designated black berets as standard issue for the regular army, Rangers switched to tan berets.
Booth picks up the hockey puck without gloves. As a trained FBI agent he should know better than to handle anything at a crime scene without gloves because it compromises evidence.