The image used for the blueprint of the B.E.A.S.T. Glove is the arm of the Pacific Rim (2013) jaeger, Gipsy Danger.
Although never mentioned in the film, the Mini-Kong's name is "Suko", which was revealed on toys. It carries significant meaning, as when written phonetically in Japanese, it can be broken down into two characters that ultimately mean, "Essential Child." Interestingly, Suko is typically a female name in Japanese and, perhaps coincidentally, is a Filipino word for "surrender."
The change in color for Godzilla's atomic breath going from light blue to a reddish tint, signifying a total boost in power, is identical to the Heisei incarnation having the far more destructive Red Spiral Ray as the sheer strength of his attack is more powerful than his default blue-colored atomic breath.
Godzilla's movements and mannerisms namely the scene where he's sleeping curled up inside the Roman Colosseum, were based off of director Adam Wingard's cat 'Mischief.'
With a net budget of $135 million, this is the cheapest MonsterVerse film to date.