Java ( 132 60)
60 characters (works also with negative numbers!):
boolean u(int n){return !(n+"").matches("^.*(.).*\\1.*$");}
132 characters (returns true for negative numbers):
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;}
with comments:
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
}
And answer that is technically correct (character count includes only the function, not global variables), but I think it's cheating, 30 characters:
boolean u(int i){return m[i];}
m[] is boolean array that contains correct answers for all 32-bit integers.