I don't believe handling 404 for pages with no extensions is the issue here. I believe the issue here is extensions that aren't ".aspx" or extension-less. For example, .asp, .htm, .gif 404s are not handled. I'm not sure if this is a Kentico issue or .Net issue.

Here's what I ended up with to handle any bad URLs for my site, as well as permanently redirect my older .asp pages to the new extensionless pages.

- In the IIS custom errors tab for your site, point 404 and 405 errors to /cmspages/handler404.aspx
- Create a custom error page (ie. ~/CMSTemplates/MySite/MyCustomError.aspx)
- Create a new Page Template in Kentico using MyCustomerError.aspx created previously
- Create a new Page in CMS Desk using the Page Template created previously (ie. /404Handler)
- In Kentico Site Manager / Settings / URLs, clear the "Friendly URL Extension" field to blank
- In Kentico Site Manager / Settings / Web Site, set the "Page not found URL" to the 404 handler page you created (ie. /404Handler)

All this accomodates the .aspx and extensionless 404 errors to your custom handler. This does nothing to accomodate .asp, .htm, .php, etc.

To do that, as well as redirect my old pages, I updated the global.asax.cs file's "Application_BeginRequest" event handler.

Here's what I added at the very beginning of that:

// This ignores the redirect for editing pages (CMS Desk)
if (CMSContext.ViewMode != ViewModeEnum.Edit){
  string strUrl = HttpContext.Current.Request.Url.ToString().ToLower();
  string strNewUrl = String.Empty;
  bool badUrl = false;
  
  // Get last four characters of the URL (used to manage non .aspx 404s)
  string lastFour = String.Empty;
  int startIndex = strUrl.Length - 4;
  if (startIndex > 0)  {
    lastFour = strUrl.Substring(startIndex, 4);
  }
  
  // Redirect About menu
  if (strUrl.Contains("/about/board_of_directors.asp")){
    badUrl = true;
    strNewUrl = "/AboutOAOT/BoardofDirectors";
  }
  // etc.... for all of your redirect pages
  
  // This catches a few page extensions that would otherwise result in the "specified file cannot be found" message
  // This just redirects to the home page in this case.
  else if (lastFour == ".asp" || lastFour == ".htm" || lastFour == ".php"){
    badUrl = true;
    strNewUrl = "/";
  }
  
  if (badUrl){
    HttpContext.Current.Response.Clear();
    HttpContext.Current.Response.Status = "301 Moved Permanently";
    HttpContext.Current.Response.AddHeader("Location", strNewUrl);
  }
}