Goofs

While it seems convenient that the Franklin worked so well for the crew of the Enterprise when the original crew was unable to repair it, there are a few things to take into consideration. When the crew of the Franklin gave up attempting to repair the ship they instead began to use the nebula and the drones to lure and attack nearby ships. If Jaylah and the aliens she saved Scotty from are anything to go by, they have been doing this for a while to a large variety of ships. We don't actually know how old Jaylah was when she found herself alone on the planet, nor how old she is now. It is entirely possible that, at the time her ship was destroyed, she was old enough to have been taught a few basics of engineering that, with time and a little natural genius not to mention extreme necessity, she was able to turn into a working a knowledge. While we don't know how long she has been there, it is obvious from her initial encounter with Scotty that she has spent at least a portion of her time scavenging parts from the ships Krall and his crew rain down on the planet and bringing them back to her "house" aka the Franklin. While it may seem surprising that she was able to repair the Franklin when its crew could not, she was only able to do so once Krall and his men, aka the Franklin's original crew, began to lure ships to the planet for her to salvage. By the time she had enough parts to repair the vessel. it is safe to assume that they had completely abandoned all thought of returning to their original ship and heading home. It is unclear exactly how much time the crew of the Enterprise spends on the planet, but at least one full day passes, the majority of which Scotty spends on the Franklin. Considering that Jaylah has spent a considerable number of years patching up the systems on the Franklin with whatever salvage she can find, and also taking into consideration Scotty's well-established genius, it is not entirely surprising that he was able to take it the last leg and repair it completely. See more