Weird behavior finding target using Physics.OverlapSphere

I'm trying to learn Unity and making a simple Tower Defense game to do it. The towers have a radius in which they can attack. I'm using Physics.OverlapSphere to find available targets and then checking which target is closest. That target becomes the target until he leaves the tower's range, after which it reruns the function to find a new target.

Almost everything seems to be working properly. I'm using gizmos to visually display the target and that works great. The only thing that isn't working is I want the tower to LookAt the object. If I set the tower attack radius (detectionRange) to a high number like 20 or more which takes up most of my map, the tower will rotate properly only when the targets get really close (5 or less). If the radius is more reasonable like 5, then the gizmos and targeting works but the tower doesn't rotate.

What am I doing wrong?

Here's the code (also since I'm learning, please feel free to tell me where I could do things better):

 #pragma strict
 
 var hasTarget : boolean = false;
 var detectionRange : float;
 private var closestEnemy : Transform;
 
 function Update () {
     
     //Makes sure we have a target
     if (hasTarget){
         //Checks the distance between the tower and target
         var currentEnemyDist : float = (closestEnemy.position - transform.position).sqrMagnitude;
         //If the target is further than the detectionRange, get a new target
         if (currentEnemyDist > detectionRange) {
             hasTarget = false;
         }
     }
     //If we have a target, rotate to look at it
     if(hasTarget){
         transform.LookAt(closestEnemy.transform);
     }
     //If we don't have a target, find one
     else {
         GetTarget();
     }
 }
 
 function GetTarget() {
     //Create a sphere with radius of detectionRange and return targets in range
     var enemiesInRange : Collider[] = Physics.OverlapSphere(transform.position, detectionRange);
     var enemyDistance : float = Mathf.Infinity;
     var colDistance : float;
     //Cycle through each target in the sphere
     for (var col : Collider in enemiesInRange) {
         //Targets must have the tag "Enemy"
         if (col.gameObject.tag == "Enemy") {
             //Check the distance from the tower to the target
             colDistance = (col.transform.position - transform.position).sqrMagnitude;
             //Finds the closest enemy
             //Checks each target to see if the next one is closer than the previous
             if(colDistance < enemyDistance) {
                 //If it's closer, set the target
                 closestEnemy = col.transform;
                 //Set the distance to check against subsequent potential targets
                 enemyDistance = colDistance;
                 //Set the tower to know it has a target
                 hasTarget = true;
             }
         }
     }
 }
 
 function OnDrawGizmos () {
     Gizmos.color = Color.blue;
     if(hasTarget) {
         // Draws a blue line from this transform to the target
         Gizmos.DrawLine (transform.position, closestEnemy.position);
     }
     //Draws a sphere to see the detectionRange
     Gizmos.DrawWireSphere (transform.position, detectionRange);
 }