Fridge Brilliance: Vimes is bemused by the fact that the Low King is "crowned" by sitting on top of a sacred relic. But dwarfs regard things that are "low" to be better than things that are "high", so putting the Scone on his head would be treating it less respectfully than his perching on top of it.
Gavin and Carrot's fight with Wolfgang. Much is made of the fact that Carrot fights "by the rules"; but when Gavin jumps in, he's trying to fight fair, too. Which Gaspode notes before he jumps in to help.
Fridge Logic: In contrast to Pratchett's usual genius with consistency and detail, the weight mechanism guarding the Scone of Stone only makes sense if you don't think about it at all. If you try to figure out how exactly it's supposed to work, you'll find its apparent principle is convoluted enough to require a computer to run it, but it would still have to be a very stupidly programmed computer.
The platform is - unseen to anyone walking on it - actually floating in an underground reservoir of water, so when you step on it (entering the Scone room), it displaces a certain amount of water, which flows into a bathtub-shaped tank on rails. When you step off the platform, that tank is shunted along a bit, and replaced by an identical but empty one. The original reservoir refills using a ballcock mechanism. The next time you step on the platform (on your way out of the Scone room), the same thing happens, displacing water into the second movable tank. If you were the same weight each time, the two tanks weigh the same now. Otherwise, one is heavier. The tanks slide sideways onto a simple scale mechanism. If there's a difference in the weights, the scale tilts, knocking a switch that lowers the cage around you and sounds the alarm-bell. Simple.
But it would be mechanically impossible for the components to move fast enough to get separate readings for Vimes, Cheery and Dee, and the system must also be able to distinguish between which of the people who went in is now coming out.
I've just re-read the passage and there is NO indication of how the mechanism actually works - there is a short comment about a hydraulic system, but that's the "boat lift", not the scales in the corridor leading to the scone. Where are you guys even finding all that detail to argue about?
That's just one hypothetical solution that probably only took a few minutes to think of. The Dwarves have had centuries to work on the problem.
Speaking of the Scone's protective mechanisms, the first part with the water-locks and boat could be Fridge Brilliance on the dwarfs' part. At first glance, it just sounds like another way of operating an elevator, but when you consider that vampires in Discworld (barring serious self-help training in the style of the de Magpyrs) have an aversion to crossing running water, you realize that it's not necessarily set up that way to keep out dwarf thieves.