Sarcasm!
When he nitpicks over another player's slip of the tongue - "
Air walk! You can't be casting
air walk!" - you say "No, Jim, I levelled that character up before the session, he's epic now" and roll your eyes.
If "Jim" isn't a complete dunce he should get the hint that silly things like this don't matter and aren't relevant.
When it comes to the spells the wizard can cast - you ought to sit down and look at his spell list, then go through and write down your rulings and adjustments for each spell he can cast. Do the same for his items. Let him read over the list and even change out spells or items he "would never have taken" given your changes. But let him do this
once, and make it clear that your rulings are final. If something comes up in later play that genuinely wasn't covered by your notes, make a thoughtful ruling then and write it down on your list.
When he wants to take new spells or make new items, make rulings on them as he acquires them, and make it clear that your rulings will apply in all circumstances.
Apart from this, make him a resource. When you can't quite remember a rule, ask him to find it for you - not
quote it, but
find it - and
quickly discuss with him and other players how it should be treated if you, the DM, don't like the rule as written. Again, once a decision is made, stick to it. Make copies of your rulings for yourself if you need a reminder.
Okay, maybe the sarcasm isn't good advice - though I would try it, because a little gentle ridicule can actually wake people up to themselves - but I'm very serious about the rest. Unless this guy is basically a cheater, having a strict set of rules he can reliably use to make plans will satisfy him immensely - and you need not ever establish a rule that interferes with your personal vision for the game.
One final thought: Make it clear that, as a DM, you will not necessarily always present the party with challenges out of the book - so if your rules lawyer has a
Monster Manual, he won't be able to object to unanticipated qualities or features of monsters or dungeons - but pledge that you'll always define the abilities of the opponents they face, even if they don't follow "the rules" and even if the players never get to see your list.
Then, having made that promise, you can keep it or not as you see fit.
