As specific as I can be:
Highest Point:
Evolution was amazing. DX was legendary. Both of those groups were staples in the WWE for years (both from storyline perspectives as well as the members themselves). I don't think either are the high point. If you have to narrow it down to one feud, angle, and match, I think it has to go to the buildup and match between himself and Mick Foley as Cactus Jack at the 2000 Royal Rumble.
The storyline leading up to match was near the top of the list for any storyline in his career. Right at the start of the McMahon/Helmsley Regime, this angle suspended the crowds disbelief enough that an actual "pull off the shirt" metamorphasis was not only believeable, but exciting as well. The firing of Foley and the subsequent "Bogus Mankind" promos were top notch in their ability to feel sympathetic with Mick (and were pretty damn funny too).
The match itself is my favorite match of all time. That's not to say that it's the best match of all time,or even close. The build up was great, the overall brutality of the match was memorable, and it told its story remarkablely. I think this was HHHs best in ring performance, and when everything is tied together is the most memorable period for HHH in my mind.
For as many highs as HHH has had, he's had a ton of lows as well. Others have mentioned a lot of post-WM25 situations, so I'll try to go a different route.
The 2nd ever Elimination Chamber with HHH defended the title against Randy Orton, Kevin Nash, Chris Jericho, HBK, and Goldberg was a pretty hyped match. I know personally I was nothing less than stoked for it; after all the first Elimination Chamber was amazing.
When the match finally starts, HHH stars in an inner chamber. When his door finally opens, he is immeditely SCM'ed stepping out of his chamber. He then stands up and doesn't participate in the match in the slightest - remaining in his inner chamber until everyone but Goldberg is eliminated. He then takes a few shots from Goldberg, gets slid a sledgehammer, and promptly hits Goldberg with it for the win.
Now, I've seen HHH put on poor matches. I give him a break as of late because he's gone through a lot of injuries and we all know he isn't what he used to be. But this one just disappointed the hell out of me - he was in his prime, it was a major title defense in a hyped PPV, and he put forth no effort whatsoever.