How to Limit Input.mousePosition or Raycast

Hey Unity,

I've been implementing mouse interaction into a grid-based game. Currently I am using a combination of Physics.Raycast with ScreenToRay and then Lerping the selectors position.

I've attached a short GIF showing that the sensitivity makes it so it's almost impossible to select the tile you want.
I am wondering if anyone has encountered this before and/or if anyone has any advice or suggestions on how to achieve a smoother more precise selector.

Here's a snippet from my scripts

RAYCAST

 Ray ray = GameCore.currentCam.ScreenPointToRay (Input.mousePosition);
         Debug.DrawLine (ray.origin, ray.GetPoint(100f),Color.red);
         if (Input_Enabled) {
 
                     
         int layerMask = 1 << 8;
 
         if (Physics.Raycast (ray, out hit, 50f, layerMask)) {
                 if (hit.collider.gameObject.GetComponentInParent<GameTile_Controller> () != null){
                             if (lastTile != null) {
                                 if (hit.collider.gameObject == lastTile)
                                     return;
                                 
                             }
                             timeStamp = Time.time + cooldown;
                             lastTile = hit.collider.gameObject;
                             GameCoreInstructions.instance.Current_Selector.GetComponent<System_SelectorController> ().currentTargetTile = hit.collider.gameObject;
                             GameCoreInstructions.instance.Current_Selector.GetComponent<System_SelectorController> ().StartLerping ();
                         } else {
 
                         }
                     }
                 }

LERP

 if (isLerping) {
 
 
             float timeSinceStarted = Time.time - _timeStartedLerping;
             float percentageComplete = timeSinceStarted / timeTakenDuringLerp;
             //Perform the actual lerping.  Notice that the first two parameters will always be the same
             //throughout a single lerp-processs (ie. they won't change until we hit the space-bar again
             //to start another lerp)
             transform.position = Vector3.Lerp (transform.position, newPos, percentageComplete);
 
             if(percentageComplete >= 1f)
             {
                 transform.position = newPos;
                 StopLerping ();
             }
 
 
         }
 
 
 public void StartLerping(){
         _timeStartedLerping = Time.time;
         isLerping = true;
         if(Current_Tile != null)
             Current_Tile.GetComponent<GameTile_Controller> ().isSelectorOnTile = false;
 
         // Go to NEW Location
         Current_x = (int)currentTargetTile.transform.position.x;
         Current_y = (int)currentTargetTile.transform.position.z;
         newPos = new Vector3 ((float)Current_x, 0.2f, (float)Current_y);
     }
 
     void StopLerping(){
         isLerping = false;
     //    Debug.Log ("finished lerp");
         Move_Update ();
         GameCoreInstructions.instance.audioSource.clip = GameCoreInstructions.instance.clips [1];
         GameCoreInstructions.instance.audioSource.Play ();
     
 
     }