Namely, why he didn't help the dwarves of Erebor when he arrived with his army (and why the heck did he just happen to have his entire army with him when he reached Erebor?) and saw Smaug rather casually wading through everything they threw in his way.
Warning: Spoilers ahead!
In the new movie, at one point Thorin gives Thranduil hell for not helping on that long-ago day. Thranduil replies that 'Nothing could have helped'. Thorin angrily responds that 'You don't know that, what do you know about dragons?'
And Thranduil responds, his glamour fading, "I know more about dragons and their fire than YOU ever will!"
Also, if you ever get a chance to look at the art book for the movie, do so. The pictures they ave of Thranduil make him look both magnificent and frightening. You get the idea that this is what Sauron might have looked like once. It's hard to describe. On one level, he looks mostly human in the picture and yet at the same time you know this this is something completely inhuman.
They also have the joking mention that Azog is one of the original orcs of Morgoth (which makes him, what, over 5000 years old?) and that 'orc teenagers probably have posters of this guy on their wall, ripping the heads off of dwarves and elves'. So... orc kids are death metal fans?
- Desolation of Smaug: this explains something about Thranduil (warning, some spoilers)