I agree with what you said about Paul, he was my first thought too, but fact is he was getting MUCH stronger and much better at working with his Pokemon as the series progressed. And his Pokemon certainly didn't seem to dislike him in any way (bar Chimchar). I would very much like to see if he's still taking the attitude of replacing weaker Pokemon with stronger ones though, if so they I don't think he'll ever be as strong as he wants. I think the weakest rival either has to be Barry or Trip. Trip has a lot of potential, but he's the only rival to have done pretty badly against Ash's team (in their third battle) - it seems like he's getting stronger at a much slower rate than Ash etc. And Barry... Well, Barry was just never that strong to begin with haha. I think he chose an awkward team to work with and he doesn't really have what it takes to be a great Pokemon trainer.
I agree with you that Barry was just generally weak, and even though he trained regularly and got all the gym badges, he just wasn't really that strong. He didn't really seem like he planned that much ahead post-battle, and he wasn't really that quick on the battlefield either, giving him small chances in the league as we saw.