Okay, so Indy and Mutt have battled evil KGB agents, decoded Oxley's secret letter and headed off to Peru.
They take pains to bring Mutt's motorcycle along with them to Peru, but Mutt never rides it again. The motorcycle, I'm guessing, is one of Mutt's sole possessions, and a central object of his identity. Act II will see Mutt losing that identity (just as he lost his "wild one" Brando hat, and his photo of himself with his beloved professor Oxley, which was inside it, in the diner) and gaining another. (We know his motorcycle rebel identity is a put-on because he doesn't go back for his hat, whereas Indy would never leave a fight without his hat.)
Detecting a lack of "heart" in Kingdom, jacksonpublick writes: "This is the same director who took 5 minutes out of his shark thriller to show an exhausted Brody bonding with his kid, and another 10 to show Brody, Hooper and Quint bonding on the Orca." As Mr. Publick is no slouch at injecting emotional truths into compact, fast-moving narratives, maybe he has a point, maybe Kingdom does move too quickly, but I found plenty of "heart" in it -- just in different places from where I was expecting to find it, and in different forms. There is plenty of interpersonal communication in the narrative, but it often turns the dynamic of the previous movies on its head (another classic Spielberg ploy). As mr_effulgence correctly notes, almost every action that we expect from Indy is inverted in this movie, from the source of his employment to his habitual actions. And so the outgoing, daring Indy we know and love from the other movies now becomes the watchful, guiding, worrisome patriarch of the new one. His actions are still active, but they are the actions of a protective father instead of a carefree young (or middle-aged) man.
The "protagonist bonding with his kid" scene happens near the top of Act II of Kingdom, as Indy and Mutt walk through the gorgeous Peruvian Marketplace set on their way to the sanatorium. On the way, they discuss Mutt's home life and the relative use of education. The first part of this conversation turns out to be important to the plot, the second part is important to the theme. Mutt craves experience, while his mom insists upon his gaining knowledge first. Seeming purely expository on first viewing, the scene picks up emotional gravity second time around.
Indy and Mutt arrive at the sanatorium, where we get a lingering glance at capital-M Madness as Mutt stares, horrified, at a mad Peruvian (a reference to a similar beat in Silence of the Lambs?). That moment, plus the interior of Oxley's cell clearly indicates that this is, thematically, the Sanatorium For Men Who Know Too Much. (Thank goodness crazy people are graphomaniacs -- otherwise, how would we ever know what had driven them crazy?) Oxley has left the extremely subtle thematic clue "RETURN" carved into the walls of his cell from top to bottom, along with several images of deformed skulls -- whatever could this elusive message possibly mean?
(A couple of readers have complained that the puzzles in Kingdom are too easy, and that Indy has no problem solving them and is never wrong. I disagree: Indy is wrong several times during Kingdom and here is one instance -- he thinks Oxley wants to return the Crystal Skull to its place of origin, when Oxley wants only to return it to the grave of the Conquistador Guy who stole it.)
Indy and Mutt venture out to the graveyard of Conquistador Guy, which is guarded by scary guys in skull masks, one of whom Indy kills (in defense) and one whom he drives off. I feel bad for the scary guys, who don't seem to be employed by anyone, but are, rather, only trying to protect the cemetery from grave robbers -- that is, people like Indiana Jones.
Inside the tomb of Conquistador Guy, Mutt finds skeletons of Mayans with deformed skulls. Indy explains that the natives would alter their skulls to look more like their gods. Mutt protests that "God doesn't look like that," and Indy answers "Depends on what your God looks like." This comment looks ahead to the revelation of who the crystal skull belongs to, but also looks backward to the atom-bomb scene. 20th-century America established its 50-year run of world supremacy on the basis of the atom bomb, and in the process killed the old god and created a new god of Technology. As the narrative of Kingdom will eventually reveal, the ancient Mayans were way ahead of the US in worshiping a technological deity.
I'm not sure now why Indy and Mutt go to the Tomb of Conquistador Guy, except that it meant a lot to Oxley. In any case, they don't find what they're looking for -- they find, instead, this Crystal Skull geegaw. (One of my companions at the movie complained that the Crystal Skull was a bad prop to build the movie around -- too big to carry in a pocket, too small to have a proper amount of gravity, and present onscreen for too long to remain mysterious. Characters have to clutch it like a baby, or grocery bag, leaving them unable to fight or climb or run.) No sooner do they get the skull but they are captured by Irina Spalko and friends, including Indy's friend/enemy Mac.
Spalko tells Indy the things he didn't know about the crystal skull, ie that it is the skull of an extraterrestrial ("E.T.!" exclaimed Sam, who only just saw E.T. a few weeks ago), and, much as she earlier forced him to look for the box in Hangar 51, now forces him to gaze into the eyes of the crystal skull. And, just as Indy was conflicted earlier by his desire to know vs. his desire to stay alive, this time around submits to the temptation of the skull -- the temptation to know.
(How extensively applied is the theme of "knowledge vs. experience" in Kingdom? That is, how badly does Indy want to know what's inside the box and what will he do to find out? To hint at the answer, Spalko is wearing a haircut inspired by Louise Brooks, who was the star of a movie titled Pandora's Box. Kingdom is, I'd say, Spielberg's most thematically dense movie after Jurassic Park.)
Indy gazes into the crystal skull (an homage to Hamlet?) and it almost fries his brain -- obviously, in the opinion of Kingdom, too much knowledge can be a dangerous thing. This is an essentially conservative viewpoint and points to the fundamental change in Indy's (and, most likely, Spielberg's) character. The young Indy was all about charging forward, taking chances, stealing fortune and damning consequences, the old Indy is about proceeding with caution, careful planning, replacing what has been taken and protecting those close to him.
He is also presented with Oxley (beforehand or afterward, I can't remember now), who has gone stark raving mad from gazing into the skull -- a preview of things to come. The "kingdom" of the title, it will eventually be made clear, is knowledge itself, and the ruler of the kingdom of knowledge must be careful about gazing too deeply into the skull -- knowledge, without experience, can only lead to amorality and death.
Spalko reveals her evil plan to Indy (your basic "rule the world" scenario, although Spalko, at least, is a patriot who shows no signs of wanting to overthrow or outlive Stalin -- more than I can say for Raiders' Belloc or Crusade's Donovan) and then demands that he help them get some sense out of Oxley. Indy refuses and is presented with Marion Ravenwood, the woman he loved and abandoned at least twice that we know of, and who is, we are told, Mutt's mother. So Indy, at the close of Act II, has acquired an almost-family, and has suddenly taken on the responsibilities of not only a mentor to Mutt but a guilty ex to Marion (and, for that matter, to Oxley). Indy's character of charging forward and leaving a "trail of human wreckage" (in Marion's words) comes careering home to him in this moment and forces a change within him -- looking out for himself vs. looking out for others.