Unfortunately, this still does not work.  The variables PLUS, MINUS,
MULTI, and DIVIDE are blank finals, and there are two rules that apply
here:

1. They must be guaranteed to be initialized by the time static
initialization is complete.

2. They must not be multiply assigned.

Both rules are applied according to the compiler's conservative
data/control flow analysis, as specified in the JLS.  The actual
contents of the array are not considered in performing that analysis.  
So the loop through the OPERATORY array is not a valid way of
accomplishing the initialization.

It's trivial to modify this code to use temporary variables, in order to
work around both restrictions on the direct use of finals.  Here is the
result:

public class Stale
{
   public static final String[] OPERATORS = new String[] {
       "+", "-", "*", "/"
   };

   public final static int PLUS;
   public final static int MULTI;
   public final static int MINUS;
   public final static int DIVIDE;

   static
   {
       int plus = -1, minus = -1, multi = -1, divide = -1;

       for (int i = 0; i < OPERATORS.length; i++)
       {
           if (OPERATORS[i].equals("+")) plus = i;
           if (OPERATORS[i].equals("-")) minus = i;
           if (OPERATORS[i].equals("*")) multi = i;
           if (OPERATORS[i].equals("/")) divide = i;
       }

       assert plus != -1;
       assert minus != -1;
       assert multi != -1;
       assert divide != -1;

       PLUS = plus;
       MINUS = plus;
       MULTI = plus;
       DIVIDE = plus;
   }
}

(Incidentally, I also removed the pointless use of "new String", and
fixed the apparent typo with the array name.)

The reason is a constructor will be called many times, at least
potentially, but a static initialiser block is guaranteed to be called
exactly once.

Java does not want to deal with the possibility of you changing your
mind about a final value.