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No she is not slow, it's a lisp. She's perfectly normal.

she has a noticeable lisp but neither the character (and presumably actress) come across as having anything wrong about them beyond that

"I don't care, I'm still free. You can't take the sky from me"

Actually, in this film she has (IMHO) the most "normal" voice she's ever portrayed. She usually is typecast to play characters where she has to exaggerate a sort of "bimbo" voice/attitude. The fairy in Scrooged, the principal in Jawbreaker, Louis' cousin (?) in an episode of Family Guy, etc.

Who hurt you, HeartMonger? Who made you sad?

Absolutely, HeartMonger!

Dude, chill. She's always had a speech impediment. So what?

That is such a stupid, contorted view that only a little child of todays day and age would think. Carole Kate does indeed always sound like that, she's pretty normal! She's also pretty damn terrific, dontcha think?
She was pretty terrific in "Dog Day Afternoon" and very believable in that film as well, albeit with a much smaller role.
She just sounds the way she sounds, and you know what? She knows how she comes off, and on "Taxi" a TV series in the 70s she guest starred as a putzy, slow person to showcase her personae. She's great. Love her.
"All I want in life is a thirty share and a twenty rating."

Carol Kane always sounds like that.