I managed to modify the set widget to fix the problem described here. 
 While I don't understand the system enough to guarantee this code is bug 
free, it doesn't break the wiki and seems to work with all my test-cases.


(I don't really know how to go about submitting this to the project...)


To use this modification, replace the content of 
*$:/core/modules/widgets/set.js* with the code below:

/*\
title: $:/core/modules/widgets/set.js
type: application/javascript
module-type: widget

Set variable widget

\*/
(function(){

/*jslint node: true, browser: true */
/*global $tw: false */
"use strict";

var Widget = require("$:/core/modules/widgets/widget.js").widget;

var SetWidget = function(parseTreeNode,options) {
    this.initialise(parseTreeNode,options);
};

/*
Inherit from the base widget class
*/
SetWidget.prototype = new Widget();

/*
Render this widget into the DOM
*/
SetWidget.prototype.render = function(parent,nextSibling) {
    this.parentDomNode = parent;
    this.computeAttributes();
    this.execute();
    this.renderChildren(parent,nextSibling);
};

/*
Compute the internal state of the widget
*/
SetWidget.prototype.execute = function() {
    // Get our parameters
    this.setName = this.getAttribute("name","currentTiddler");
    this.setFilter = this.getAttribute("filter");
    this.setValue = this.getAttribute("value");
    this.setEmptyValue = this.getAttribute("emptyValue");

    // Set context variable
    this.setVariable(this.setName,this.getValue(),this.parseTreeNode.params);

    // Construct the child widgets
    this.makeChildWidgets();
};

/*
Get the value to be assigned
*/
SetWidget.prototype.getValue = function() {
    var value = this.setValue;
    if(this.setFilter) {
        var results = this.wiki.filterTiddlers(this.setFilter,this);
        if(!this.setValue) {
            value = $tw.utils.stringifyList(results);
        }
        if(results.length === 0 && this.setEmptyValue !== undefined) {
            value = this.setEmptyValue;
        }
    }
    return value;
};

/*
Selectively refreshes the widget if needed. Returns true if the widget or any 
of its children needed re-rendering
*/
SetWidget.prototype.refresh = function(changedTiddlers) {
    var changedAttributes = this.computeAttributes();
    if(changedAttributes.name || changedAttributes.filter || 
changedAttributes.value || changedAttributes.emptyValue
        || (this.setFilter && this.getValue() != 
this.variables[this.setName].value)) {
        this.refreshSelf();
        return true;
    } else {
        return this.refreshChildren(changedTiddlers);       
    }
};

exports.setvariable = SetWidget;
exports.set = SetWidget;

})();


On Friday, 18 September 2015 13:15:41 UTC-5, Evan Balster wrote:
>
> Note that the issue with <$set> not refreshing occurs regardless of 
> whether a value/emptyValue condition is used.
>
> On Friday, 18 September 2015 10:00:44 UTC-5, Tobias Beer wrote:
>>
>> Despite the limitations, I have added the example here...
>>
>> Conditional Variable Assignment @ tb5 
>> <http://tobibeer.github.io/tb5/#Conditional%20Variable%20Assignment>
>>
>> Best wishes,
>>
>> — tb
>>
>

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