My "four conceptual hangups with HPs":
1) I can buy modeling heroism with escalating HP... and natural healing makes more sense now too. But the fact that healing becomes LESS effective (i.e., doesn't scale with HP) with level doesn't match the model and sort of feels wrong to me.
2) Invincibility - being held at knifepoint or faced down with a dozen crossbow wielding guards all the sudden isn't much of a manipulation technique against high level characters, and jumping off cliffs becomes a viable options. Yeah, some heroic models fit this, but I think by default it's a little over the top.
3) Up or down - You never show the effects of your injuries until 0 hp. Until then, you receive no penalties. Any after a knock down drag out fight, you usually are just spiffy the next day.
4) Heroic sages - Linking HP to level works for me for PCs -- its a growth of heroic prowess. But when it comes to NPCs, it doesn't work so well. The greatest cook or sage in the world need not have more HP than a 1st level commoner AFAIAC. (Oddly, the only d20 branded game that really tries to correct this is Star Wars.)
The other side of this coin is, yeah you can correct these, but any correction tends to add enough complications that it's generally not worth it. I came up with a solution to #3 that works for me (no tables, one roll determines both save and results, can often ignore, results proportional to damage, but it requires you be good at doing math in your head.), but the rest I live with.
I wouldn't even begin to suggest that HP DON'T WORK. If they didn't, given these problems, they would be outa here.
The manyshot/shot on the run (and dual strike/spring attack) ruling strikes me as not being the implicit result of the RAW and lawyeristic hair splitting.
Sauropods, due their immense HD, have better reflex saves than cats.
But really, there are a ton of rules that if you over-analyze them, fall down under inspection. (Hong's law, anyone?), but the sort of thing that really bugs me are rules that REALLY have an impact during play.
The biggest one that comes to mind is the iterative attack rule. I would rather prefer that all attack rolls had the same modifier. Iterative attacks at high levels require you to specifically remember which dice roll goes with which attack modifier, which sort of forces the DM to stop and process every attack individually while waiting for the player to do the math. I work around this one too, but I don't like it. Let's just say, this is one thing I dig about spycraft.