A lot of what this season is really about, like the "Ice and Fire" novel it's based on, "A Storm of Swords," is the mighty being brought low, and the inevitability of that in the order of things. That's why hacking off Jaime Lannister's sword hand isn't just a gratuitous horror. In an instant, this most charismatic of blonde-god egomaniacs has his crucial source of pride and dignity removed. Freudians would have a field day with this, although it could be argued that process dismemberment truly began when he was defeated in what I guess you'd have to call hand-to-hand combat by the splendid Brienne.
It's worth cutting off that hand, in other words, just to see how Jaime will fare without it, and how his perspective will shift, over the next few weeks. In storytelling terms, that's more than enough to justify the act.
In general, the characters in Martin's novels who don't thirst and grapple for power are the ones who are valorized, though a failure to recognize that others are doing so behind your back is certainly a weakness, Ned Stark being cautionary example number one. Tyrion, in that sense, is the story's proper central character, being level-headed, sympathetic and crafty all at the same time.
Too sensible to take the game entirely seriously, even though he plays it well, the Little Big Man has one of his better moments in Episode 3, wincing and fretting at the prospect of replacing Petyr Baelish as the Lannister administration's Master of Coin. We sense, however, that Tyrion is doing a Br'er Rabbit number, here, careful to object strenuously to the very outcome he's hoping for, since this is the office that was such a formidable power base for Littlefinger. Time will tell.
The scenes with Tyrion, Bron and Pod in this episode are flat-out comic relief, a welcome first for this rather grim season. When Pod is offered his reward in the brothel the show runners seems to be addressing the horny 14-year-old-boy contingent in the audience: "You're grumbling that there hasn't been enough nudity this season? Well how about this? And this. And this! That oughta hold you for a while."
In the payoff scene a bit later on Pod comes across as the Dirk Diggler of Westeros, the innocent stud who doesn't know his own strength. We're keeping our fingers crossed that poor Pod never gets his source of power chopped off.