I would forgive the whole "she's the dumb" one premise if it had only been part of the premise. If she had learned a little from being around the boys, and didn't always say such stupid things, that would be okay. If she was shown to have hidden "smarts," like, say, a great understanding of Shakespeare, Ibsen or Oscar Wilde (she is an actress anyway, and this could easily tie into why she chose to become an actress.) Or have her "smarts" be artistic ones, which again could be tied to her decision to be an actress. The sad thing is that they haven't even allowed her to be a good actress on the show; she can't even seem to catch a break or at least perform a scene that proves to the audience that she too is worthy of our admiration.
The other thing I'd like to see is her romantic life take a more sympathetic approach. She is always dating jerks (Leonard included), but we know immediately as audience members they are jerks. In real life, when guys turn out to be jerks, it usually starts out in a small way, sometimes in ways that friends do not even notice, and then near the end of the relationship (or when the relationship should end) it explodes into something big and awful. I want the writers to seduce the audience with what looks like a great guy and fails to be, fails in a monumental, terrible, heart-breaking way. That way, we understand that Penny doesn't just date awful guys because she's too stupid to know better, but because these guys are liars, and good ones. Watching this show, I imagine the writer's room filled with guys angry at that one pretty girl who would not go out with them, and here they are, getting revenge on her fictional counterpart, dismissing her as stupid, making fun of her womanliness, and then forcing her into bad relationships with guys who do not love her and just want to sleep with her (again, Leonard included, who could not be bothered with her beyond her physical appearance.) In some ways, that is far too much like straight women's experiences with men, and why so many men do not deserve the women they turn on after they have been rejected. If a man gets rejected gently by a woman and then turns into that kind of monster, then that that monster is who is always was. He would have just behaved that badly in some other way to her later on. 
More than anything, I honestly do not watch the show much because of the flaws around Penny (and the continued trashing of Sheldon, who is far more interesting that Leonard, Raj and Howard combined.) But do you know what's surprisingly good? The Big Bang Theory fanfiction. The fanfiction, written mostly by women, I've noticed, allows Penny to have a certain amount of depth and generally doesn't sink into the dumb stereotypes the show has such a habit of doing. My favorite group is Paradox. I am frequently impressed with the writing that goes on over there. I honestly wish these ladies were the ones writing the show. 