You'd be surprised how many problems are 'solved' but only barely. I use software that I hear people complain about every day. They have pretty sales webpages but the software itself is buggy, slow, hard to use, and support is unresponsive. Just make something 10% better and you would make a killing.

I'm avoiding mentioning a product or category not just to avoid throwing someone under the bus, but because I can think of many examples of this. None of the software (or any other kind of product) that I use today was the first of their kind. They learned the lessons from the earlier versions, and did it better.

Even if every problem you can think of has been solved (and I'm skeptical of that), I'm sure you don't think that all existing software is already perfect. Pick something that's terrible, and do it better.