When plotting the path of the Kaiju to Mt. Fuji, it shows them heading in from all three sides. However, they are then first seen stood together in Tokyo, meaning two must have navigated around the volcano to get there.
When talking to Scott Eastwood's character and making a bowl of ice cream, John Boyega's character starts out with the whipped cream bottle in his right hand. In the next shot (behind John Boyega), it's in his left, and then the shot after that it's back in his right.
When Shao Industries Shanghai HQ is introduced for the first time on screen, a map displayed on the left pinpoints the location somewhere near Weihai, a relatively small coastal city in Shandong province of China. The actual location of Shanghai is about 700 km south from Weihai, on the eastern seaboard and mouth of the Yangtze river.
With the final boost into the atmosphere, the pilots are warned that Gypsy Avenger could burn up on re-entry. Then Jaeger is shown burning up, however, even with a hole through the visor, the two pilots remain unaffected.
The film posits that the Precursors' ultimate plan was to reach Mount Fuji and all the cities they leveled were just in the way. This makes no sense, as the kaiju attacked cities all across the Pacific, most of which are in the complete opposite direction.
Put simply, Stacker Pentecost never had a son. He said his adopted daughter Mako Mori, was "all he had" in Pacific Rim (2013). Jake Pentecost was never mentioned, seen, or even hinted at in Pacific Rim (2013) or any of the comics.
Jake Pentecost says in a pep talk that when he was a kid, he "jumped into a Jaeger". a character asks how far he got, and he finally answers "a few steps". It is impossible that he got into the Jaeger at all, as they require an entire team to start them up, not to mention that he would need to be wearing a special suit with the modifications installed by another team. Without this suit he would of not been able to connect to the Jaeger at all.
The goof item below may give away important plot points.
When the surprise attack occurs at Sydney Harbor, a rogue Jager rises from the water directly in front of the Sydney Opera House. Sydney Harbor is not a deep water harbor and is less than 50 feet deep near the Opera House. Jagers are nearly 300 feet tall, so it would be impossible to conceal a Jager in that location.