Define "'creative' ideas".

Do you think improving your critical thinking capacity would help?

I think what might be more benefit is insight. More often a little is gained during the education phase, programming languages and design, be it institutional or self taught. For some it's hard to come by, not everyone thinks and works outside the box that well or is comfortable there. The rest comes via experience, your own as well as if you are fortunate enough, to see how others approach a problem and the processes used to arrive at the solution / end product.

I'm unsure if by creative you mean a fancy new feature that only the latest and greatest OS or browser supports. I'd be happier if more web designers included or kept in mind some backwards compatibility, ie for text based browsers and those who browse without JS.