Traditionally the best man can be a bit of a loose cannon. He's the guy you've selected to celebrate you in just the right way, probably a lifelong friend or brother, but deep down you're not too sure if he's going to over step the mark. A large proportion of best men speeches around the world still seem dead set on destroying lives, not realising that the most significant casualty of all, will be themselves. However, there's not much you can do about a speech once it's set in motion, but you can mitigate and limit the damage as much as possible. I simply don't agree with brides demanding to have a first draft of the best man speech and signing it off on their approval, if you're that unsure about the guy, don't choose him in the first place. Just make sure he sticks to a sensible word count, and leaves out the former girlfriends - the very worst that can then happen is that he recounts a few dodgy stories, but doesn't outstay his welcome.
However, when it comes to how you should mention the best man in your groom speech, then that needs a careful eye as well. Many grooms spend far too long talking about their best man, in fact, it's not uncommon for the best man and bride to have equal footing in the speech, and that's just plain wrong. You should limit your best man to around a couple of sentences in your speech, anything more than that and you're going down the tedious story route which bloats the speech to a 35 epic. Also mention your best man in the middle of your speech, not at the end. I never understand why so many people insist on making the handover to their best man as the crescendo to their groom speech. Get the MC to do that - the pinnacle of your groom speech should always be about the bride. Period.
So, have a quiet word with the best man to make sure he's sticking to a decent length of speech, make sure he's not toasting his way to oblivion, and remember that he really isn't nearly as important as the bride!