In previous chapters, we saw the downside of having a fellow like the Master of Laketown in charge. In this chapter, we see the downsides of having people like Bard or Thorin in charge. In fact, this could really have been an opportunity for the Master of Laketown to shine, stepping in to mediate between Bard and the Elvenking on one side, and Thorin (and later Dain) on the other. Instead, we hear a brief reference to the Master of Laketown by Bard, who claims to be speaking as representative of him. Most likely, this is just Bard claiming to be doing everything in the name of the theoretical authority, and the Master is just thinking about how to escape with a piece of dragon hoard when he gets the chance.
Bilbo is, of course, appalled by the turn of events. With Smaug dead, he is thinking he gets to fill his pack with some payback for all his efforts, and head home at last. More intriguing is the question of what Gandalf is thinking. Clearly, he is not too keen on Thorin's behavior, but he cannot be all that much happier about Bard and the Elvenking. Perhaps, having seen the devestation wreaked on Laketown and its people, he is having a harder time sympathizing with Thorin's position. Or, perhaps he can simply tell they are in no position to be reasoned with. Every time Bard returns to his camp to see his folk freezing and starving, it probably stokes his anger. Gandalf is not great at fast talk, and he may know when to simply say nothing.
Of course, it's possible, given the very small numbers of the dwarves, that Bard was considering a frontal assault. Being only 13 in number (Bilbo is not likely to have been willing to fight on the ramparts against the people of Laketown), it is entirely possible that with a few wooden screens to shield their approach the men (and perhaps elves) could have forced their way in. Perhaps Gandalf convinced them to try siegecraft instead, hoping to buy time for tempers to cool.
Regardless, and because we learn of things from Bilbo's perspective we don't know much about what was being discussed in the camp of the elves and men, it is a chapter that says, 'the dragon may be dead, but the enemy is not defeated yet'. The dragon's hoard is turning out to be more destructive than the dragon, even.
Chapter 16