I'm still waiting to hear what from the newer stuff is so incredibly unbelievable.
OK, I'll bite.
#1 The Enterprise warping to Vulcan in minutes to hours instead of several days at least.
#2 Vulcan collapsing into a blackhole and the Enterprise in orbit remaining uneffected.
#3 Spock being able to see Vulcan with the naked eye when he's in another solar system.
#4 Kirk's escape pod landing walking distance from Spock.
#5 Scotty's outpost being walking distance from Spock.
#6 Scotty being able to beam himself and Kirk to the Enterprise flying away at warp.
Moving onto Into Darkness.
#1 The Enterprise hiding under water instead of high orbit.
#2 They hide the Enterprise, but not the shuttlecraft?
#3 Stopping the volcano is already interfering with the culture, seeing the Enterprise is a much smaller deal than preventing extinction.
#4 Why did Kirk and Scotty swim down to the engineering hull instead of an airlock close to the bridge? They would have lost consciousness before swimming that deep and died.
#5 Why does the Enterprise have side-mounted torpedo launchers like an old sailing ship?
#6 Why does it take 20 torpedoes flown across the Klingon empire to take out one man?
#7 How is the Enterprise in the Neutral Zone and in orbit of the Klingon home world at the same time?
#8 Why didn't the Klingons see the Enterprise?
#9 Why didn't Kirk know who Khan is?
#10 Why did the Vengeance get so close to the Enterprise?
#11 When the Vengeance shot the Enterprise, the Enterprise could have slammed into the Vengeance, killing everyone.
#12 Why did 20 torpedoes exploding inside Vengeance not destroy the entire ship instantly?
#13 How did the Enterprise parked dead by the moon suddenly fall toward the Earth?
#13 Why did the Enterprise falling out of orbit (thought it was over by the moon) take so long?
#14 Why was Kirk's death scene ripped off from TWOK instead of doing something new?
#15 If Khan's magic blood can bring back Kirk, has death now been cured?
#16 The ending: Khan wins, he destroyed like have of San Franciso.
#17 Why is the Enterprise crew remembered with no mention of the deaths of everyone else?
This is just the first 2 movies of the reboot trilogy. It keeps going into the third film and the streaming shows.