It's been a while since I've seen it, so you might be right about certain specifics being a bit far-fetched (and I do remember it getting a bit too close to "the truth is unknowable anyway"). So maybe in this specific case Fonda's character is stretching the definition of reasonable doubt, but that's not because it's a parody, I (reasonably) doubt you really believe that. The reason is simply that it makes for better suspense : you're presented with what seems like unsurmountable evidence and then you see Fonda's character tear it apart, which I found to be very enjoyable. It sounds like you didn't really think he was effective at tearing some of those apart, fair enough.
As for your specific points : discrediting witnesses is a thing, you must be aware of that right ? Maybe the glasses thing is a bit far-fetched, but it's something that happens all the time in those situations, and with reason : people's memories are unreliable. That doesn't mean you can't ever trust a witness because you'll always find something : you don't have to go from one extreme to the other.
There's also another aspect in 12 Angry Men, which is the death penalty. The reason Fonda has a pretty loose definition of what constitutes reasonable doubt also has to do with the, well, final quality of the sentence.