That whole sequence, while adorable and definitely giving good intro for Wash and Mal, really just sets up an awesome tracking shot that will introduce the cast. If you know the architecture of the Serenity, you know that Mal's going to have to literally visit every part of the ship in order to go yell at Kaylee about the entry couplings or whatever, which you know he's going to do, because no matter what happens, he will always yell at Kaylee about the entry couplings or whatever. He loves his ship more than anything, but like with anything else he loves, he has no idea what's going on inside her.
Jayne, the muscle, comes running out into the corridor. "We're gonna explode? I don't wanna explode!" Mal wants him focused on the crisis immediately after the one where they explode, the robbery job they're planning planet-side. Mal will distract you so fast. "Jayne, how many weapons you plan on taking? You only got two arms." Jayne explains that he gets "excitable as to choice," and likes to have his options open. It's a nice pointer to both his capacity for violence and the fact that all he loves is guns. And his lovely hat, which we'll see a bit later. Mal explains that the plan for this job doesn't include shooting, and Jayne notes that what Mal plans and what usually takes place "ain't ever exactly been similar." Mal can't argue that, but tells Jayne he can't bring any grenades, causing him to whine like a baby.
Zoe, first mate, Mal's war buddy from the fight for independence, my personal favorite character, appears: "We crashing again?" Mal tells her to ask her husband, who is the pilot, Wash, and asks if the Mule is prepped -- that's the four-person ATV they use on the ground. In the Big Damn Movie, it flies. Mal, and the tracking shot, continue into the kitchen as Zoe and Jayne trail off, still talking about the grenades: "We're robbing the place, we're not occupying it..." Into the engine room, where adorable, wonderful Kaylee is running around, calm and efficient as a cucumber with an engineering degree, as the interior of the engine room goes to merry hell all around her: sparks, smoke, buzzing, beeping, freaking. "Kaylee! Kaylee, what in the sphincter of hell are you playing at? We got the primary buffer panel coming right..." She smiles. "Everything's shiny, Captain. Not to fret." Behind her, the room is almost entirely obscured by smoke and steam, and sparks are shooting out of everything. Mal complains that she told him the entry couplings would hold for another week, and she reminds him that this conversation actually took place six months ago. Hmm. Wonder how long Inara's been gone?