Again, jumping around to random items...
Health care: I also see it as the AMA's fault. They're a private company that can have a doctor arrested for, basically, not paying them dues. They intentionally limit the number of doctors available to each area AND fix the prices. They set the malpractice requirements (thereby setting insurance costs) and are often the sole arbiter in a problem. But no, the clear solution is to force everybody to pay for medical insurance (and change the insurance business model so as to require an increase in cost), rather than just fix the supply/demand disparity. (Anybody who's interested in this sort of thing should take a look at the "barefoot doctor" movements in China and India. That would be my solution.)
Grammar and Spelling: As they say, language specifications are descriptive, not proscriptive (unless you're French, in which case, l'Academie Francaise has kidnapped your guinea pig). That said, the further you deviate from formal written language, the less you should be surprised that people aren't taking you seriously. Working within the rules shows respect for the audience. That was the trouble with California's "Ebonics" experiment. It's not that kids shouldn't speak how they wish among their peers, but rather that you're raising a bunch of inner city kids to be incapable of handling a job interview. You no gots getting it solid-like, but me can gots it assuming your ignorance extend'll beyond grammarz, y'know?
(That's at least doubly true on the Internet. Any modern writing course should seriously emphasize that, when there are no other social cues available, your treatment will be based directly on what CAN be seen--your e-mail address and your writing style.)
Noun Gender: For the Romance languages, at least, blame Latin and be thankful Rome collapsed, with all its declensions and other forms. Gender (and it's only a coincidence that the system's also used for male and female people) is a simplified version of that system, I believe. I'm not sure where that originally arose, though it seems to be a common trait to all older languages (the northern European languages case nouns as well), so it might just be an artifact of pulling different groups together under a single banner--each has different rules and vocabularies, and those winning out as official are random.
You can see a similar effect in most European languages by conjugating the common verbs. For example, "to be" in French (etre, with a circumflex/caret over the first letter) has present tense forms suis, et, est, sommes, etes (circumflex), and sont. That irregularity probably tells some history about three or four tribes with different verbs; you can see relationships between etre/etes and maybe et/est, sommes/sont, with suis hanging out alone...and by the way, since et and est sound the same (/ay/), French requires every sentence to carry a noun, like English ("it's raining") and unlike Spanish, where "soy" is a valid and comprehensible thing to say ("I am").
Sequential Math: Yes, some books do use different terms, to top it off, though that's usually the "Integrated" curriculum, which is different...somehow. It's apparently a concession to the idea that kids aren't going to use it anyway, so scaring them with "real" words is silly. Because that doesn't hamstring them if they ARE going to use it. Naw. But don't worry, college kids aren't left out of this excitement, because they have the competing Harvard Calculus, which is a numerical approach based on graphical calculator use. To be fair, it has some really good ideas like focusing on visualization of function behavior, but the very thought that you can get most of the way through a calculus course and not know what a Limit is or how one might differentiate a function makes it seem counterproductive.
Differential Equations: I haven't had a professional use for them, personally, but then my career has involved programming trouble management, warehousing, and provisioning software, where the most complicated math is generally subtraction of integers. However, I have friends in fields like air conditioning design and nanotube applications, so it's typical "dinner conversation."