Sorry, wrong mod. You're, of course, insightful.

For anyone with actual experience with control systems, this looked pretty much spot on. The only oscillations just above critical damping were in the throttle value, and SpaceX acknowledged as much. I don't know what you really know, but it doesn't seem like much.

The rocket didn't come in unstable, it was pretty much following the barge avoidance reversion trajectory. The thrust output was unstable, but given that the trajectory was quite spectacular. Remember that for the rocket to end where you want it to be, you need to precompensate by turning the whole body sideways, so that you'll have countertorque for sideways thrust when retargeting to the barge. That seemingly large and "weird" excursion was completely normal. Try it out in KSP if you must, and remember never to throttle down beyond TWR=2.2.

That thruster did the correction, but there was literally no leg for the thing to stand on. One or two of the legs have collapsed on landing. A bigger thruster would simply keep it upright until the nitrogen ran out (here it didn't), it'd still fall and go kaboom.

Sorry, they met #1 and #2. The vertical velocity at contact with the barge was as close to zero as anyone could wish for. That's the only one that matters, given that it's a system with thrust-to-weight ratio > 1. The on-contact vertical velocity was lower than the vertical velocity on 95% of commercial transport airplane landings when the wheels touch the pavement. You'd be really surprised at how good this landing otherwise was, given the just-about-oscillating thrust controller issue that they had.

These explosives are actually hard to set off. If I gave you some, and you had nothing explosive in your house, you actually couldn't set them off.

The explosions aren't massive. The amount of propellants involved is rather small. As far as rockets-going-boom, this is nothing. Also remember that rockets used in warfare often carry conventional warheads that have an order of magnitude more stored energy than the propellants do. So even if the entire thermal energy from the propellants was converted to kinetic energy of the rocket (a thermodynamical impossibility) and delivered in the entirety to the target, it'd still be pointless.

TL;DR: That barge could withstand a fire from a large LOX and LH2 spill, but it wouldn't withstand a single hit from a 50x lighter rocket designed to actually damage things by going boom.

Imagine that the net has to catch a bulldozer with a long, empty soda can rigidly attached to it. The weights and relative strengths involved are similar. Your objective is to not crush the can. Now you know why they didn't do it.

They were a part of a pre-planned hole-punch-avoidance maneuver. It was a part of the plant. Imagine what would happen if the engine didn't restart, with the rocket aimed at the middle of the barge. Hence you aim outside the barge, start the engine, then re-aim to the X. I bet that they trust the engine enough by now that they'll get rid of that maneuver in the next landing or two.

An aside: If you really, really wished to, you probably could use something as simplistic as a PID, except that there'd be a nonlinear, time varying transform applied to its inputs, and its outputs. At that point you can pretty much almost implement any controller you wish while still claiming that there's a PID in there somewhere :) Think of the Park and Clarke transforms used in motor controllers. The overall controller still uses a PID core, but behaves nothing like a raw PID would. The transforms could be much more complex, effectively implementing a whole different control scheme, and letting PID not do much of substance :)

The "rotation of the entire vehicle" part was because the scenario, currently, is:

1. Use aerodynamic lift and grid fins to aim to the side of the barge.

2. Start the engine.

3. Re-aim to the middle of the barge.

They do this since they still fear that a relight might fail and the heavy octaweb structure will punch a hole through the barge. It may well be that the next landing will be aimed at the bulls eye already during the final, unpowered part of the descent.

It can be. We've already seen it done. The difference between success and failure in this most recent case has been very slight. It doesn't take any major redesign to fix that sort of a thing. Get real.

Sorry, that should have read: humans controlled translation, rotation and thrust level. The automation also decayed the roll rates to zero, so that if you'd reorient, it'd stay that way by itself.

The moon landing was with human-in-the-loop, but it was automatically stabilized and would have been impossible otherwise IIRC. Had the automation failed, they'd have to abort back to orbit. An automatic controller kept the thrust vector going through the vehicle's center of mass. The humans controlled the orientation and thrust level.

Probably the part you're not aware of is what the immigration lawyer does once you decided to hire such a candidate.

It's not a perception, it's a reality, and yes, the workers have zero power.