At the 6:46 mark into the episode, when Mobius is giving a brief about all the different variants of the Loki, they have tracked so far. In the wide shot, the variant number of the first 'Blue' Loki is "L1247," but at the 6:49 mark, in the next close up shot, it switches to the "L6792," and the same variant number "L1247" is shown with the next "tour de France Loki."
Listing the destruction of Pompeii as apocalypse level event is factually incorrect. A majority of the residents who lived there fled the city and survived as the actual destruction of the city took place over 2 days and not as quickly as depicted.
When the Vesuvius volcano explodes, the sound of the volcano is heard in Pompeii immediately. However, sound take 5 seconds to travel 1 mile, and Mount Vesuvius is 14 miles distance from Pompeii.
In Roxxcart during the hurricane apocalypse, the shelves were completely stocked. Under normal circumstances during a disaster, store supply shelves would be empty or, at the very least, untidy.
In the Pompeii-scene, there is a Roman numeral visible on the wall: LXXIX, which is 79 in decimal notation. This may indicate the year 79 AD, in which the Vesuvius volcano erupted. However, counting the years was not in use at that time, as years were named after the ruling consul and were not numbered sequentially. It is far more likely that the number on the wall has a different purpose, possibly representing a house number. The fact that it happens to be the same number as the year of the event (according to modern time reckoning) could just be a coincidence, or a deliberate Easter egg placed by the filmmakers.
Tom Hiddleston's microport is clearly visible under his tie, as he talks to Owen Wilson's character by the elevator.
The fossilized remains of many inhabitants of Pompeii have been discovered, very well preserved due to the Volcanic ashes, and they are studied by archaeologists. By intruding in their lives right before the eruption Loki would have caused them to die in different places or positions, which should have caused a time variance.