Here is the code where I use currentEditingReference as a global variable.
 Below I will also put the code where I 
tried to hand currentEditingReference to the 2nd function as an argument. 



function moveDeleteControls(e) {
    // 10-01-06 - at the top of this file, you'll see this function
    // assigned to the documents onmouseover event:
    //	document.onmousemove= getMouseXY; // getMouseXY(event) implied on NS, getMouseXY(null) implied on IE
    //	document.onclick= getMouseXY;
    //	document.onmouseover= moveDeleteControls;
    //	var tempX = 0;
    //	var tempY = 0;

    if (!e) var e = window.event;
    if (e) {
	var eventTargetRef = e.target;
	if (!eventTargetRef) eventTargetRef = e.srcElement;
	var targetsClassName = eventTargetRef.className;
	window.status = targetsClassName;
	// 10-15-06 - originally the yellow delete box had only one option, and
	// and that was deletion, so we tested to see if it was of class "deletable".
	// I'm not sure this check is worth it any more. 
	if (targetsClassName == "interact_editable") {
		// 2012-02-23 - change back the style on the currentEditingElement to its previous state, 
		// before we update what the currentEditing Element is.
		if (currentEditingReference != null) {
			backupStyleInfoObject = arrayOfDomElementsWithTheirPreviousStyleAttributesRemembered[currentEditingReference.id]
			currentEditingReference.style.backgroundColor = backupStyleInfoObject.backgroundColor;
			currentEditingReference.style.borderColor = backupStyleInfoObject.borderColor;
			currentEditingReference.style.borderWidth = backupStyleInfoObject.borderWidth;
		}
		
		// 2012-02-23 - new we update which DOM element the currentEditingReference is pointing to
	    currentEditingReference = eventTargetRef;
	
	    currentEditingReference = addUniqueIdToAnElement(currentEditingReference);
		storeTheOriginalCssAttributesOfThisDomElement(currentEditingReference); 

	    // 2012-02-21 - now we change the current ref so as to highlight it
	    currentEditingReference.style.borderColor = '#00FF00';
	    currentEditingReference.style.borderWidth = '2px';
	    currentEditingReference.style.backgroundColor = '#FF0000';
	    moveBoxToMouseCoordinates('delete_box');
	}
    } else {
	window.status = 'No event found in moveDeleteControls';
    }
}





and this: 



function storeTheOriginalCssAttributesOfThisDomElement() {
	// 2012-02-23 - when we mouseover and editable item we change some of its CSS attributes
	// but when we mouseover the next editable, we want to restore this one to its original
	// CSS values, so we store them here. 
	var backupStyleInfoObject = new BackUpStyleInfo(); 
	backupStyleInfoObject.backgroundColor = currentEditingReference.style.backgroundColor;
	backupStyleInfoObject.borderColor = currentEditingReference.style.borderColor;
	backupStyleInfoObject.borderWidth = currentEditingReference.style.borderWidth;	
	arrayOfDomElementsWithTheirPreviousStyleAttributesRemembered[currentEditingReference.id] = backupStyleInfoObject;
}








And then below is the code where I tried to hand in the variable as a function argument:




function storeTheOriginalCssAttributesOfThisDomElement(referenceToDomElement) {
	// 2012-02-23 - when we mouseover and editable item we change some of its CSS attributes
	// but when we mouseover the next editable, we want to restore this one to its original
	// CSS values, so we store them here. 
	var backupStyleInfoObject = new BackUpStyleInfo(); 
	backupStyleInfoObject.backgroundColor = referenceToDomElement.style.backgroundColor;
	backupStyleInfoObject.borderColor = referenceToDomElement.style.borderColor;
	backupStyleInfoObject.borderWidth = referenceToDomElement.style.borderWidth;	
	arrayOfDomElementsWithTheirPreviousStyleAttributesRemembered[referenceToDomElement.id] = backupStyleInfoObject;
}

function moveDeleteControls(e) {
    // 10-01-06 - at the top of this file, you'll see this function
    // assigned to the documents onmouseover event:
    //	document.onmousemove= getMouseXY; // getMouseXY(event) implied on NS, getMouseXY(null) implied on IE
    //	document.onclick= getMouseXY;
    //	document.onmouseover= moveDeleteControls;
    //	var tempX = 0;
    //	var tempY = 0;

    if (!e) var e = window.event;
    if (e) {
	var eventTargetRef = e.target;
	if (!eventTargetRef) eventTargetRef = e.srcElement;
	var targetsClassName = eventTargetRef.className;
	window.status = targetsClassName;
	// 10-15-06 - originally the yellow delete box had only one option, and
	// and that was deletion, so we tested to see if it was of class "deletable".
	// I'm not sure this check is worth it any more. 
	if (targetsClassName == "interact_editable") {
		// 2012-02-23 - change back the style on the currentEditingElement to its previous state, 
		// before we update what the currentEditing Element is.
		if (currentEditingReference != null) {
			backupStyleInfoObject = arrayOfDomElementsWithTheirPreviousStyleAttributesRemembered[currentEditingReference.id]
			currentEditingReference.style.backgroundColor = backupStyleInfoObject.backgroundColor;
			currentEditingReference.style.borderColor = backupStyleInfoObject.borderColor;
			currentEditingReference.style.borderWidth = backupStyleInfoObject.borderWidth;
		}
		
		// 2012-02-23 - new we update which DOM element the currentEditingReference is pointing to
	    currentEditingReference = eventTargetRef;
	
	    currentEditingReference = addUniqueIdToAnElement(currentEditingReference);
		storeTheOriginalCssAttributesOfThisDomElement(currentEditingReference); 

	    // 2012-02-21 - now we change the current ref so as to highlight it
	    currentEditingReference.style.borderColor = '#00FF00';
	    currentEditingReference.style.borderWidth = '2px';
	    currentEditingReference.style.backgroundColor = '#FF0000';
	    moveBoxToMouseCoordinates('delete_box');
	}
    } else {
	window.status = 'No event found in moveDeleteControls';
    }
}








Have also tried to create a new object and copy some of the style info over:


function moveDeleteControls(e) {
    // 10-01-06 - at the top of this file, you'll see this function
    // assigned to the documents onmouseover event:
    //	document.onmousemove= getMouseXY; // getMouseXY(event) implied on NS, getMouseXY(null) implied on IE
    //	document.onclick= getMouseXY;
    //	document.onmouseover= moveDeleteControls;
    //	var tempX = 0;
    //	var tempY = 0;

    if (!e) var e = window.event;
    if (e) {
	var eventTargetRef = e.target;
	if (!eventTargetRef) eventTargetRef = e.srcElement;
	var targetsClassName = eventTargetRef.className;
	window.status = targetsClassName;
	// 10-15-06 - originally the yellow delete box had only one option, and
	// and that was deletion, so we tested to see if it was of class "deletable".
	// I'm not sure this check is worth it any more. 
	if (targetsClassName == "interact_editable") {
		// 2012-02-23 - change back the style on the currentEditingElement to its previous state, 
		// before we update what the currentEditing Element is.
		if (currentEditingReference != null) {
			backupStyleInfoObject = arrayOfDomElementsWithTheirPreviousStyleAttributesRemembered[currentEditingReference.id]
			currentEditingReference.style.backgroundColor = backupStyleInfoObject.backgroundColor;
			currentEditingReference.style.borderColor = backupStyleInfoObject.borderColor;
			currentEditingReference.style.borderWidth = backupStyleInfoObject.borderWidth;
		}
		
		// 2012-02-23 - new we update which DOM element the currentEditingReference is pointing to
	    currentEditingReference = eventTargetRef;
	    currentEditingReference = addUniqueIdToAnElement(currentEditingReference);
		var newObjectToStoreDataFromCurrentReference = currentEditingReference.style; 
		newObjectToStoreDataFromCurrentReference.id = currentEditingReference.id;
		storeTheOriginalCssAttributesOfThisDomElement(newObjectToStoreDataFromCurrentReference); 

	    // 2012-02-21 - now we change the current ref so as to highlight it
	    currentEditingReference.style.borderColor = '#00FF00';
	    currentEditingReference.style.borderWidth = '2px';
	    currentEditingReference.style.backgroundColor = '#FF0000';
	    moveBoxToMouseCoordinates('delete_box');
	}
    } else {
	window.status = 'No event found in moveDeleteControls';
    }
}


Amazingly, I'm now getting "currentEditingReference is undefined" on this line: 

                var newObjectToStoreDataFromCurrentReference = currentEditingReference.style;

but I just defined it 2 lines earlier.