Well, it looks like I answered my own question.

The change that I made yesterday did in fact introduce a side-effect. The problem is with
this segment of code in line 457:

// And lastly -- if the template begins with @@, treat it as a function
if (formattedItem.substr(0,2) == "@@")
   formattedItem = eval(formattedItem.substr(2));

Now I understand why apostrophes, quotation marks, etc. were being escaped. My changes
from yesterday caused the eval function to fail and thus throw a JavaScript syntax error. This
made the DNN Solution Explorer to stop functioning.

Below are the changes that I made to the RssInfo class in the file
/Resources/FeedBrowser/scripts/feedbrowser.js. The RssInfo class begins at line 422
(including comments):

////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// BEGIN: RssInfo class                                                                                       //
// Defines the structure for a single RSS feed                                                                //
////////////////////////////////////////////////////////////////////////////////////////////////////////////////
DotNetNuke.UI.WebControls.FeedBrowser.RssInfo = function(feed, template, header, allowHtml)
{
    this.formattedItems = [];
    var itemCollection = feed.value["items"];
    var feedHeader = [];

    if (header)
        feedHeader[0] = header;
        
    for(var item in itemCollection)
    {   
        var itemData = [];
        if (typeof(itemCollection[item]) == "object")
        {
            var ivalues = DotNetNuke.UI.WebControls.Utility.recurseElement("", itemCollection[item]);
            for(var iv in ivalues)
                itemData[iv] = ivalues[iv];
        }
        else
            itemData[item] = itemCollection[item];
            
        var formattedItem = template;
        
        // If the template is a function (i.e. begins with "@@") then treat it differently
        // as we would a normal HTML template
        if( formattedItem.substr(0,2) == "@@" )
        {
            // First pass -- replace data tokens surrounded by [[ ]]
            for(var attribute in itemData)
            {
                var dataValue = (allowHtml ? itemData[attribute].xmlEntityReplace() : itemData[attribute]);
                // Replace the token with the actual data value
                formattedItem = formattedItem
                    .replaceAll("[[" + attribute + "]]", dataValue
                    .replaceAll("'","'")
                    .replaceAll("\"",""")
                    .replaceAll(",",",")
                    .replaceAll("\n"," "));
            }            

            // And lastly -- since template begins with @@, we treat it as a function        
            formattedItem = eval(formattedItem.substr(2));
        }
        else // Normal template
        {
            // First pass -- replace data tokens surrounded by [[ ]]
            for(var attribute in itemData)
            {
                var dataValue = (allowHtml ? itemData[attribute].xmlEntityReplace() : itemData[attribute]);
                // Replace the token with the actual data value. Do not do any special processing
                formattedItem = formattedItem.replaceAll("[[" + attribute + "]]", dataValue);
            }
        }

        this.formattedItems[this.formattedItems.length] = formattedItem;
    }
    
    this.formattedItems = feedHeader.concat(this.formattedItems.sort());    
}
DotNetNuke.UI.WebControls.FeedBrowser.RssInfo.registerClass("DotNetNuke.UI.WebControls.FeedBrowser.RssInfo");
// END: RssInfo class