Your right, I hadn't seen the problem from that angle. So you mean it would be better to do something like the following one :

for(int i : arr){
    if(i < min) min = i;
    if(i > max) max = i;
}

Great. Thus, as you can see, you can much more simplify your algorithm :p

I don't understand why you need to iterate through all array elements so many times while you can just do something like that :

 public static int[] findHighLow(int[] arr){
        int largest = arr[0], smallest = arr[0];

        for(int i = 1; i < arr.length; i++){
            largest = Math.max(arr[i], largest);
            smallest = Math.min(arr[i], smallest);
        }
        return new int[]{smallest, largest};
    }