Continuity mistake: Azog kills Fili with his arm sword, running him through from back to front. In the next moment, when Azog tosses the dying Fili off the ledge, we see the arm sword - and it is shiny, clean and spotless.
Continuity mistake: When the dwarves finally decide to leave Erebor and join the battle, they swing a giant gold pendulum into the blockade they all made earlier in the film, knocking it over to create a causeway, across which they all then run in a battle formation, straight into battle. However, just as they all exit the keep, the pendulum is on its downward swing back outside of the wall. In all following shots (from numerous different camera angles) the gold pendulum simply disappears. This is most notable in the shot taken directly in front of Thorin as the dwarves run towards the camera. The pendulum should be visible in the large hole in the wall behind them, but instead the hole is empty, with no pendulum to be seen.
Continuity mistake: During the battle, when Legolas throws Thorin's sword into the troll above Thorin, he pulls the sword out and it is stained with blood. But seconds later, when Thorin is walking on the ice, the sword is completely clean.
Continuity mistake: The number of dead Orcs on the ice as a result of Legolas' arrows changes from significant to small in one shot from his point of view.
Revealing mistake: When the master's gold falls into the water off his boat, several of the gold items can be seen floating, something no gold item should. (00:40:00)
Revealing mistake: When Gandalf shakes Bilbo's hand it should be a lot bigger than his but it is the same. (02:25:26)
Deliberate mistake: Conan Stevens' character in this film is an unnamed orc who briefly attacks Gandalf and is defeated by Galadriel. However, in the first movie, the same character briefly appears in the flashback to Moria and is credited as "Bolg." This is due to the role of Bolg being recast and the two remaining filmed scenes of the original actor being repurposed. The filmmakers originally intended for first film Bolg to be a younger Bolg, but later retconned this, despite already crediting him as Bolg.
Revealing mistake: During the battle of Dale, Bard confronts Alfrid, who is dressed as a woman and is trying to escape with looted gold. During the confrontation a troll climbs over the parapet and is killed by Bard. As the troll falls, Alfrid also falls. When he lands, the ground near his hand ripples like fabric covered in sand.
Answer: Aragon is 87 in LOTR: Two Towers (as mentioned in the extended edition). The Hobbit takes place about 60 years before that so Aragon is 27 at the time. Sauron is banished to Mordor in Battle of the 5 Armies. You see his "spirit" flee and the White Council, mention he went back to the east. Between Sauron and Sarumon, it's mentioned more in other LOTR books, but Sarumon (while still technically good) has been looking for the One Ring. He does not join Sauron as much as uses the alliance for his benefit hoping to find the ring first.