Need your are help, m in tricky situation. Potential customer wants access to private beta. If he likes it, straight way he want to use it for their production.
Product is not yet very polished from UI prospective. As they said first impression matters ,What should i do ? Shall i give customer access as it is or wait for some time ?
If they don't like it, you can always email them / call them to have a second look when you feel you've made noticeable progress.
EDIT: If using it in production carries a lot of risk for this customer, don't pussyfoot around and advise him to wait.
Congratulations. You're basically getting early feedback by someone who really really wants this. He wants a beta to use in production, and he knows that. That's how much he wants it.
Lay down the ground rules as far as production support and bug fix turnarounds based on what you can manage without trying to spend every waking minute keeping them happy. They may not get every new feature request they ask for, and , like you said, some UI might change.