Continuity mistake: In the barrel riding scene just after Kili is shot in the leg, Tauriel arrives carrying her bow in her left hand. In the next shot the bow is in her right hand: she nocks, draws, and shoots with her left hand. (00:50:20)
Revealing mistake: When Smaug confronts Bilbo and weaves around the gold in his lair, as the dragon asks "What else do you claim to be?" his tail passes through one of the pillars (audience's left).
Continuity mistake: When we first see Alfrid with the Master of Laketown, he is talking about the rebellious people. On his left shoulder is a big splat of yellow goo, probably from a thrown egg. In the previous scene, where he confronts Bard and tries to have the barrels of fish dumped in the water, he hasn't got the yellow goo on his shoulder yet. In the extras of the Extended edition it is revealed that there was a scene filmed where Alfrid was pelted with eggs by the townsfolk when he walked to the Master's house, but the scene was not included in either the theatrical or the extended version. The egg also explains his line: 'the mood of the people is turning ugly'. (01:09:35 - 01:11:35)
Continuity mistake: In the theatrical version of the first movie, Smaug is shown stomping into Erebor with his front legs. In this movie, it is revealed that Smaug does not have front legs, and that he instead has claws on the ends of his wings. This was corrected in the extended edition of the first movie, but remains a mistake in the theatrical version.
Factual error: The melting point of gold is nearly 2000 degrees Fahrenheit, and yet Thorin rides a wheelbarrow through a river of molten gold with his fingers inches away from the stream. Even if we believe the dwarfs are hardier than men, I doubt he could survive that, let alone the wheelbarrow.
Chosen answer: Bilbo is actually quite clever, I think he was trying to talk his way out by buttering Smaug up. If he tried to run, Smaug, who was on high alert, would have caught him and swallowed him without a second thought. By playing with words he was able to both interest and distract Smaug, and get away.