Yes.
The writers of TNG were clearly aware how old Alexander is supposed to be...
Ronald D. Moore was aware of it, but Ronald D. Moor didn't directly write the Alexander stories in TNG.
Just because it's not spoonfed to the audience doesn't mean the writers or producers made a mistake, they're just not providing what should be pretty obvious information.
Which, IF that was something they actually thought through as a plot point, would be relevant.
But Alexander didn't go through Soap Opera Rapid Aging because of (or in order to establish the fact) that Klingons age faster. It happened because filming an episode with a one-year-old Klingon toddler would be dramatically unsatisfying since Alexander would be WAY too young to really understand what just happened to his mother and wouldn't be able to bond with Worf in that context.
Basically: Alexnader's rapid aging had nothing to do with his being a Klingon and everything to do with Duras killing K'Ehleyr. The fact that he would need to be at least four years old for the story to work the way it does is all the explanation we need for why that error went (deliberately) uncorrected.
What next, if the new series doesn't make a direct reference to oxygen in the first season are you going to say that no where in the new series is it canon that the characters are breathing oxygen because it was never said so on screen?
That depends. If one character mentions that the engine room has decompressed and thirty seconds later we see a couple of people walking around IN the engine room without space suits or breathing gear, I'm going to expect that somewhere between those two scenes it is established that the engine room now has oxygen.
But sometimes they screw up, and the two scenes run back to back, and that particular plot point either doesn't get filmed or doesn't make it into the actual episode, or the space suit props they planned to use for that scene turn out to be cumbersome and horrible and they reshoot the scene without the space suits but then forget to change the earlier line about the room being decompressed. When that happens, we call it a "continuity error" and then we, the fans, make up a bunch of satisfying and well-reasoned rationalizations after the fact in order to maintain our suspension of disbelief, just like you're doing now.
What continues to puzzle me is why you keep chiming in to claim that continuity errors AREN'T continuity errors just because you can come up with an explanation for them. This is like me saying "There was a spelling error in this morning's news paper" and you saying "How's that an error? Everybody knows what that word is
supposed to be. Maybe they spelled it wrong on purpose just to be funny?"