The party montage on top of the Hotel at 38.32 shows a still of Dr Brennan in a red enclosed resting area. The laptop, clothing and people surrounding her indicate this was filmed at the same time as her video conversation to Angela shown earlier. Dr Brennan is shown moments later in a different outfit.
The opening car scene in LA with Booth and Brennan were filmed the same day as later in the show (around the 31 minute point) when they are in the car discussing the newest facts of the case. It is obvious this is the same day because the actors are wearing the exact same clothes as the earlier scene.
When Booth is waiting for the woman to talk to her at the end of the episode he has his hands clasped and in his lap but in the next scene he has them by his chin.
When referring to the Iron Age warrior, almost all of the characters mention that he lived 1500 years ago. However, the start of the Iron Age proper is considered to fall between around 1200 BC and 600 BC, depending on the region (1200 BC - 1 BC in Europe, where the remains were found), thus making the skeleton 2000 years old at least.
The rental car in California is a 1965 Mustang, not a 1966.
Goodman was somehow able to work out the warrior is a Pict based purely on his face, which is not a metric used when investigating the origin of a skeleton.
Addtionally, the skeleton was buried in Southern England, but earlier in the episode it was stated that the remains are 1500 years old from the "Iron Age", when the Iron Age in Britain ended in AD43.
The skeleton is seen to be wearing a replica of the belt buckle from the Sutton Hoo Ship Burial, dated ~620s CE, and Thor's hammer pendant, but the Vikings did not invade England until the ~780s CE.
6 minutes in, Zack says the body is 1.88 meters and Daniel says 6'1". It's actually 6'2".