Shufti's reunion with her fiance... Johnny, she hardly knew ye. To explain: "Johnny, I Hardly Knew Ye" is a classic folk song about a soldier, once a womanizer, who returns home unrecognizable because of his many horrible injuries. But here, Shufti refuses to recognize him because she's moved on.
The first time Polly lies to Maladict about herself, it's mentioned she feels her heart speeding up "as it always did when the lies came." In Thud!!, we learn that vampires can hear hearts beating and use that to judge how people are feeling. No wonder Maladict was onto her right away.
Jackrum's reason for getting stuck on recruiting party despite his in-universe Memetic Badass status: he got his leg sliced open, then bit the doctor who tried to treat him, and tended to the injury personally, allowing Froc to slap him with recruiting duty as a "reward" while he was laid up. While it's easy to pass off as a throwaway gag to enhance Jackrum's Badass status, it becomes foreshadowing when you realize that to treat his leg, the (presumably male) doctor would have either had to take Jackrum's pants off, or at least get close enough to notice that there were one or two things either missing or sock-enhanced. No wonder Jackrum bit him and did the work himself!
There's also a throwaway reference to a soldier talking about the time his dad got in a bar fight with Jackrum, and Jackrum apparently shrugged off getting kicked in the nadgers, which means he's either got Balls of Steel, or as it turns out, Jackrum doesn't have that sort of equipment.
And why is Jackrum so big? Yeah, the whole 'jolly fat man' thing is handy for Obfuscating Stupidity, but it's also a convenient way to hide her chest.
In fact, it's a pretty natural development that Jackrum got so fat: as she confesses to Polly, she was "never really a wall painting", showing her a portrait of herself and her beau before they went off to war. In fact, much like Lancre, Borogravia is just the sort of place to breed Brawn Hilda types; in a tough, harsh climate dependent on farming, a big and beefy woman who can easily handle livestock is much more useful, and much like in Lancre, Borogravian men undoubtedly regard fat women as beautiful, since they clearly must be very good at cooking.
Nuggan was nothing more than a side joke in The Last Hero, a god whose followers Offler pities because he banned chocolate and garlic. But in Monstrous Regiment we find out he is a dead god, and all the the things he "abominates" are nothing but the echo of a dead god
It may be that the events of The Last Hero led to that state of affairs; Offler pitied his followers then, and it got even worse afterwards.