US military personnel are shown using Beretta M9s (US Military designation of the civilian Model 92F/FS, etc) which were not issued as sidearms for the US Military in 1970. The 92 wasn't designed until 2 years after this movie is set, and the side arm wasn't issued till 1990.
F-16 aircraft are shown at the airbase (along with more period-correct scooters, albeit in incorrect color schemes and location) but this was set 3 years before they were designed and first flew. The F-16 didn't enter US service until 1980.
There is a Hello Kitty on the counter at the restaurant where the three council members have their meeting. The movie is set in 1970 Tokyo, but the distribution company, Sanrio, didn't introduce Hello Kitty to Japan until 1974, and that was in the form of a vinyl coin purse.
After Saya leaves the train station, we next see her in her hotel room desperately drinking from her bottle of blood. Problem is, she's wearing the school uniform, which she doesn't receive from Michael until he goes to see her with information of her next mission.
After Saya hides Allison under a wicker basket, Allison draws the wicker threads aside to see the fight better. Then there's a shot from inside of the basket, and the threads are on their original positions. After some time there's another shot like that ant the threads are spread like they should be.
In the scene where Saya, Alice and the army truck fall down a ravine, there is a part where the winged demon flies away and turns for another attack run. You see Saya jump on the side of the truck sword in hand, then see the demon flying away then cuts to Alice shouting "Saya!" and she throws the sword up to Saya. But we'd just seen Saya already had her sword.