When Liwen arrives at her Shanghai headquarters, the Shao logo disappears from her handheld device between takes.
When fighting the Kaiju, after losing both of Gypsy Avengers swords, the next shot of the pilots show the holograms of the swords still attached.
As Jake and Nate are in the kitchen talking Jake squirts canned cream onto his ice cream treat the cream canister swaps hands throughout the scene.
During the final battle it shows Mount Fuji directly next to Tokyo. In reality Mount Fuji is 130 km away from Tokyo and can easily be seen in the distance on a clear day.
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 Gipsy Avenger could burn up on re-entry. The Jaeger is shown burning up, however, even with a hole through the visor, the two pilots remain unaffected, since they are protected by their pilot suits.
When Gipsy Avenger reached the maximum height with the rocket boost, Jake and Amara should have become unconscious. The Conn-Pod is damaged and exposes them to the low-pressure environment, but their control suits are still protecting them, and providing breathable air for them.
A mirrored parking sign is briefly shown when a Jaeger is thrown away by the Kaiju in the Tokyo battle.
The scene when Shao Liwen entered the building near the 50 minute mark, the map showed that the building is in Shandong China but the announcement was in Cantonese, a dialect which is spoken more than 1000km away.
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.
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, 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 not have been able to connect to the Jaeger at all.