Character snapping to new position upon "play."

Are there any scripts attached to your objects?

Unlikely but you never know - make sure none of its colliders are intersecting with the ones on either side before you play the scene.

Colliders are not intersecting, but thank you nonetheless for that.

I do have a script applied to it. Ugh, I wish I understood this better. This is a scene that I have inherited from someone else, and I am trying to change it around to use for a different activity. This is what the script looks like. I do not have a scripting background, so bare with me please. (removed variables introduction to reduce character count). HERE IS THE SCRIPT

Can you please post your script here on the page using the "code sample" button?? Just type it in and select it then press Ctrl+k and it will format it right. I can't open that file from my office computer.

Let's see if this works...

 #pragma strict
 var theDwarf : GameObject;
 var detect : detector;
 var scriptHolder : GameObject;
 var nowActive : boolean;
 var activeNow : String;
 var intersecting : boolean;
 var lookAtPoint : Vector3;
 var dwarfSelected : boolean;
 var markedCorrect : boolean;
 var whereAmI : GameObject;
 var isPivoted : boolean;
 var isPivoted2 : boolean;
 var pivot : Vector3;
 var entrance : Vector3;
 var hidingPlace : Vector3;
 var shortName : String;
 var startingPointPos : Vector3;
 var startingPointRot : Quaternion;
 
 function Start(){
     scriptHolder = GameObject.Find("00-scripts");
     detect = scriptHolder.GetComponent(detector);
     lookAtPoint = Camera.main.transform.position;
     lookAtPoint.y = 0.0;
     pivot = GameObject.Find("pivot").transform.position;
     entrance = GameObject.Find("Entrance").transform.position;
     hidingPlace = GameObject.Find("Hiding Place").transform.position;
     theDwarf = gameObject;
     startingPointPos = gameObject.transform.position;
     startingPointRot = gameObject.transform.rotation;
 }
 
 function On$$anonymous$$ouseDown(){
     if (!detect.is$$anonymous$$oving)
     {
         detect.cutAckAnim = true;
         detect.activeDwarf = null;
         detect.activeSlot = null;
         nowActive = false;
     }    
 }
 function On$$anonymous$$ouseUp () {
     if (!detect.is$$anonymous$$oving)
     {
         detect.cutAckAnim = false;
         detect.activeDwarf = theDwarf;
         nowActive = true;
         detect.activeNow = gameObject.name;
         theDwarf.transform.LookAt(lookAtPoint);
         dwarfSelected = true;
         shortName = theDwarf.name.Substring(0, theDwarf.name.length-6);
         detect.shortName = shortName;
     }
 }
 
 function Update()
 {
     if (detect.goingTo$$anonymous$$ovies && !isPivoted)
     {
         theDwarf.transform.LookAt(pivot);
         theDwarf.transform.position = Vector3.$$anonymous$$oveTowards(theDwarf.transform.position, pivot, Time.deltaTime * detect.speed);
         if (theDwarf.transform.position == pivot)
         {
             isPivoted = true;
         }
     }
     else if (detect.goingTo$$anonymous$$ovies && isPivoted && !isPivoted2)
     {
         theDwarf.transform.LookAt(entrance);
         theDwarf.transform.position = Vector3.$$anonymous$$oveTowards(theDwarf.transform.position, entrance, Time.deltaTime * detect.speed);
         if (theDwarf.transform.position == entrance)
         {
             isPivoted2 = true;
         }
     }
     if (isPivoted && isPivoted2)
     {
         theDwarf.transform.LookAt(hidingPlace);
         theDwarf.transform.position = Vector3.$$anonymous$$oveTowards(theDwarf.transform.position, hidingPlace, Time.deltaTime * detect.speed);
     }
     if (theDwarf.transform.position == hidingPlace)
     {
         detect.areDwarvesInside = true;
     }
     if (detect.isReset)
     {
         gameObject.transform.position = startingPointPos;
         gameObject.transform.rotation = startingPointRot;
     }
 }