Heck, it should have been a one minute conversation, which it was:
"Pete, you smell like a Saigon whorehouse, and you slept in your clothes - you gotta fix that"
Pete doesn't fix it.
"Pete, you gotta go"
As I said...crisis of management in the US. From what I've read here, it looks to me like your duty to fix it is to yourself because failing to fix it make you look bad and it wastes your time. You spent a lot more than 10 minutes fixing the results of the failing to do this well. I feel differently, I believe a manager has a duty to the people who work for him. In management terms, we're on opposite ends of the spectrum, but it doesn't change that it's important to manage your people effectively.
I don't know Pete, so I don't what words would worked, but obviously these weren't it. What is critical to change the future is to identify the behavior, identify the impact that the behavior has on a positive work environment and then get a commitment from the person to own and change the behavior in the future. And you have to explain it in ways that they care about.
For example if I was talking to you about this issue, I might say "SD, man, there's a problem. Your clothes are sloppy and you have intense body odor. Nobody wants to be around you because you stink and it is impacting your ability to be successful and advance here. This cannot continue. This is your problem, what are you going to do to fix it?" That sounds harsh to a lot of people here, but I'll bet not at all to you...in fact it probably sounds a bit tame. But it's there - the specific issue, the impact explained in a way I think you care about and then asking you to own the problem and fix it.
If you had a different personality, I would have explained it using different words - say if you were the classic laboratory scientist, then I might say that the odor and sloppy clothing makes people question your professional competency and the quality of your work. Nobody sees all the great work being done because it is eclipsed by the social blunders. Same message...very different words to account for a different motivation. I would bet this version doesn't have any impact on you at all, but there are some out there who read this and reacted very strongly.
Bottom line, you were ineffective, you failed to correct the behavior and therefore you had to waste your time firing the guy and then waste more time hiring his replacement. Take, it don't take it, but it's all on you.
Crisis of management.