Java (132)
====

    boolean unique(int n){
        int[] p=new int[]{2,3,5,7,11,13,17,19,32,29};//list of 10 first primes
        double a=9001312320D;//10 first primes multiplied
        while(n>0){
            a/=p[n%10];//divide by (n%10+1)th prime
            n/=10;//divide n by 10, next digit
        }
        return (long)a==a;//if a is integer then n has all digits unique
    }

or

    boolean u(int n){int[] p=new int[]{2,3,5,7,11,13,17,19,32,29};double a=9001312320D;while(n>0){a/=p[n%10];n/=10;}return (long)a==a;}