the characters are often obtuse and whiny not because of their personalities but because the script uses this as an excuse for actual drama.
Funny, this is exactly what I find wrong with today's television, and why I refuse to watch anything made now, with the exception of The Simpsons.
I think you are making the same mistake most viewers (typically the younger folks) make: you are applying contemporary standards to a show made almost fifty years ago. If you do that, of course it's not going to compare. You need to watch it (or anything else really) with no expectations other than being entertained. That is, after all, what a TV show is for. Well, that, and to sell products of course.
Once you do that, you might find that you enjoy a show alot more, regardless of the time it was made.