This is really up to you. Without being disrespectful to those who are bi-polar, if you catch him on a good day, and word it right, then of course you could inform him that his mission statement doesn't flow correctly when translation. That it would benefit from re-tweaking, and you could do it (on your own time) and see it you can improve it.
If you catch him on a bad day, you're fucked.
The safest strategy is to do exactly what he wants, that goes for any employer, BUT when you hand in the final draft, put footnotes on that look like positive, constructive criticism... or reword it without telling him, if you're clever enough (not disrespect to you) it will still say what you want it to, and he will think they are his own words.
I need to clarify, a very dear family friend is bipolar it's part of him, on a good day he's the most generous (of spirit) accommodating and wonderful person, on a bad day beware. My parents turned up at his home one evening, after being invited to stay for the weekend... they were told to fuck off at the door. We always have a plan B so they had a lovely weekend in the Lakes instead... another time they turned up (invited) and were treated like royalty.
We never know how we'll be received, and I think the fact you suspect he may be bipolar needs to be taken into account when you decide how to deal with it.
Saying all THAT there's a chance YABU, I know a complete twat who runs a business, who's advertising is AWFUL, who actually delivers naff all and is all about the spiel, every word he utters in business or real life makes my toes curl yet... and yet, people seem to lap him up, he's hugely successful, ridiculously so!
Tough one! Is there a happy line you can walk?