I thought Grant was FAR better in THE AWFUL TRUTH and HIS GIRL FRIDAY. Both of those films are a lot better than BRINGING UP BABY, which was something of a letdown once I watched it all the way through.
Odd thing: It flopped at the box office when it was released, but like "It's a Wonderful Life" and "The Wizard of Oz" it picked up steam over the years.
I saw "Baby" the 1st time and thought it was an OK movie, but over the years I have come to LOVE it. It is now considered by film critics as the quintessential screwball comedy.
Why don't you watch it again? And keep an eye on the excellent supporting cast. (especially Charlie Ruggles)