No one extolling the value of women's intuition and tea leaves is the intellectual equal of a person said to be a extraordinary detective with years of experience.
I can't believe you're taking those wisecracks as literal, sincere statements of her methodology. She often found things out from her connections to Commissioner Gordon or Alfred, or through her work at the Gotham Library, and naturally she didn't want to reveal her sources lest they provide clues to her identity. So she gave facetious answers when asked how she figured something out.
And nobody's denying that the character was required to conform to certain gender stereotypes. Obviously we wouldn't have gotten Xena or Korra in 1967-8. Progress gets made incrementally. At the time, those feminine tropes that stand out for us today would've been routine and expected, and what would've stood out for audiences at the time would be the ways in which she rose above conventional feminine roles -- her fearlessness, her smarts, her skill at a "man's job," etc. If our modern expectations have moved beyond her, it's because she was one of the characters that started the progress in that direction. It doesn't make sense to dismiss the progress she made just because she didn't make it all the way to 2014 levels.