Personally, I think Paul was the best thing to happen to the DP anime. His rivalry with Ash felt like more than just a clash of two trainers on the battlefield, it was a total clash of training styles. It was great to see a recurring character who was such an opposite of Ash.
I don't see a problem with how his story was resolved, either. Paul was never rude to anyone for no reason whatsoever. He got annoyed at Ash because Ash kept on berating him about his style - honestly, it looked to me like more often than not, Ash was the one saying "your method of training is completely wrong" rather than the other way around. He got annoyed at Maylene because as a Gym Leader, he felt that she had provided a disappointing challenge and was unworthy of her position. He got annoyed at Dawn because a) she berated him about his style in the same way that Ash did, and b) he naively assumed that coordinators had no talent for real battles. He got annoyed at Chimchar because no matter what he tried, it didn't show the power that he knew it was capable of. These are the four that I remember from DP, and although you may think that some of these reasons were logically flawed or that they didn't make him a particularly nice guy, you have to admit that they're there. Paul did not just go up to your average guy on the street and call him a worthless piece of trash. At the end of the series, he complimented Ash because he has gained respect for him due to Ash's victory in their league battle. Since Ash had never really come close to beating him before, Paul found it hard to take him and his training methods seriously until then (he had likely not met someone who opposed his methods so vehemently before).
His training style was, without a doubt, extremely harsh. But Paul did not see it as cruel because in the end, his Pokémon got stronger and he got results. Raising strong Pokémon is a big part of being a trainer aiming for the Pokémon League, and this was all that Paul was focused on. And a lot of his Pokémon responded well to his method. He didn't develop much of an emotional connection with them, but this is Paul - he never developed much of an emotional connection with anyone. With Chimchar he made the mistake of pushing it way too far - he did this because he knew Chimchar had potential, and he tried to draw it out the only way he knew how. It was hurting Chimchar, but in the end Paul believed that it would all pay off. He was arrogant in believing that Pokémon, rather than his training method, were the ones at fault. But he did not abuse Chimchar because he relished inflicting pain on it or anything - he put it in dangerous situations in the belief that they would draw out Chimchar's strength.
At the end of the day, Paul was an arrogant guy with a method of training that disconnected him from his Pokémon emotionally, because he believed that pushing them to their limits was the best way to make them stronger. I think these characteristics made him interesting and a great rival for Ash.
