However, what I meant was, are Dutch speakers, on the whole, as poor at using Dutch as Americans are at using English? And so on for the French and French, Spaniards and Spanish, etc...

Well, I can't speak for all those languages, but I can speak for Dutch. And the the answer is a big YES.

In the days when I was still in school grammar and spelling was actually taught. Now it isn't anymore. And this shows. A lot.
I'm not claiming to be the best writer in the world, but when I see the stupid mistakes that are often made I can't help but think : "are you doing this on purpuse or are you really that dumb?"
Nah, the school system hasn't improved much in the last years. In my days at school making certain mistakes (which I won't elaborate on now, otherwise I'll have to teach you the basics of Dutch and this will end up to be a VERY long post ) was considered to be a deadly sin. Now the same mistakes are considered more or less "normal".

I still can't stand to watch them though. I guess I got that hammered in hard when I was a kid.
And so it should be. The native language is part of who you are. If this gets neglegted, it feel to me as if the whole heritage gets negleted. And that's truely a shame.