Paul's story was wrapped up just fine. I see nothing wrong with Paul's training method as well. Ash and Chimchar actually deserved the attitude Paul gave to them to not warrant any sort of punishment for that said attitude.
To start things off, Paul was a strict trainer, a trainer to whom Pokemon means business, not some creatures to goof around or building friendships with. Ever experienced military training? I see a resemblance of Paul to that of a drill sergeant (damn, ninja'd by deathseer), where Paul expected tasks accomplished by his troops under his command. There was virtually no room to slack off. The Pokemon that fit in Paul's training method prevailed, the rest had no place in Paul's roster. Chimchar didn't fit the bill, in other words, it was just a crybaby and couldn't handle Paul's training method. Why couldn't it just activate blaze when Paul asked to? If you want a place in Paul's team, you gotta earn it. Chimchar failed to do that. Instead it resorted to a worry-free abode under Ash's hood.
Secondly, Ash deserved to be treated the way he was treated by Paul. Ash was just a stubborn a
ss whose only motive after encountering Paul for the first time was to prove that Paul was wrong in his training method, despite getting his butt handed to him by Paul in consequent battles. Ash did prove him wrong, but that moment didn't highlight until the league battle, did it? If Paul was happy with his training method, I don't see how it's any of Ash's business to barge his nose in to tell him otherwise. Oh wait, it was Ash who wants to be friends with every Pokemon he encounters, rather than training them well to either win a major tournament or to reward us with some impressive battles. Mind you, I'm not saying that Ash hasn't given us any impressive battles to watch, but the count could have been more.
Lastly, there is no difference between Ash's method of training Pokemon and Paul's method of training method, though, the difference could be subtle. Paul's method was pretty much outright to us. Recall that in the league battle when Infernape crashed to the ground, despite Infernape being in pain, Ash commanded it to hang on to activate blaze, so to speak. Normally in situations like this Ash would not proceed further in a given battle, but this one can be seen as an exception. This is not any different than how Paul tried to activate Chimchar's blaze.
I also sort of visualized that Paul would just walk away after getting defeated by Ash in the league. Like you know how Paul shows respects to stronger trainers, if defeated by them, admits the defeat and move on. It would have been more fitting to his character if he said something along the line of "You were lucky", then walked away with dignity with the pride in mind that he's still the better trainer than Ash. However, giving props to his Pokemon - especially Electivire even after losing to Infernape - and acknowledging Infernape's obvious improvment and its strength after losing to Ash weren't half bad either.
See above, and please be kinder to a Pokemon responsible for the single most well-written arc of the entire anime. Nothing in the previous 650 episodes can match the Chimchar story, how it was presented, and its denouement. Nothing.
To each their own. While Chimchar/Infernape's story was well written, I don't think it was the "single most well-writter arc of the entier series"
...in my opinion (don't wanna get flamed for not stating the obvious).