We were running the latest version of the Community Edition and recently upgraded to the Professional Edition.  I worked for us on both versions.

What's occuring when you try to add the tweet module to your page?

Make sure you do the following:
Within your DesktopModules folder, create a folder named TweetModule.  Then create a new Tweet.ascx file within this TweetModule folder and enter the code below (obviously without :CODEBEGIN: and :CODEEND:) into this page and save it.  Maybe try creating a Tweet.ascx.vb file as well.  Enter the vb code below and save the file.

Next, within your host settings you need to add/create the extension to your host.  Goto Host -> Extensions and at the bottom select Create New Extension.

For Select Extension Type, select Module.
Name and Friendly Name are required fields so enter info here. Click Next.
Module Specific Details Page is next.  Usually I don't enter any info here. Click Next.
Owner Details page is next.  Enter whatever information you wish here. Click Next.

Extension has been created.  Either scroll down to the module or filter by Module type to see the newly created module.
Click the Edit extension button (pencil icon).  Under Module Definitions, add a new definition.  Add a friendly name and create the definition.

Under Module Controls, add a Module Control.
Using the drop down for Source, find DesktopModules/TweetModule/Tweet.ascx.  Click on update.
Then Update Extension.

Next, create a new page and drop this new tweet module into the page and you should then begin seeing tweets from Bill Gates's twitter acount.
Change the billgates in line }).render().setUser('billgates').start(); to the twitter account you wish to follow.

Hope this helps..  -Jeff

Tweet.ascx
<%@ Control Language="VB" AutoEventWireup="false" CodeFile="Tweet.ascx.vb" Inherits="DesktopModules_Tweet_Tweet" %>

<div id="Tweet">
<script src="http://widgets.twimg.com/j/2/widget.js"></script>
<script>
new TWTR.Widget({
 version: 2,
 type: 'profile',
 rpp: 10,
 interval: 6000,
 width: auto,
 height: 600,
 theme: {
shell: {
 background: '#333333',
 color: '#ffffff'
},
tweets: {
 background: '#000000',
 color: '#ffffff',
 links: '#4aed05'
}
 },
 features: {
scrollbar: true,
loop: false,
live: true,
hashtags: true,
timestamp: true,
avatars: true,
behavior: 'all'
 }
}).render().setUser('billgates').start();
</script>
</div>


Tweet.ascx.vb
Imports DotNetNuke
Imports System.Web.UI
Imports DotNetNuke.Entities.Modules
Imports DotNetNuke.Security.Permissions

Partial Class DesktopModules_Tweet_Tweet

    Inherits DotNetNuke.Entities.Modules.PortalModuleBase

End Class

Great, I'm glad it works for you..

Yea, I was having an issue trying to get the tweeks working and tried a number of different free tweet modules; none of which worked properly..  This was the only way I found to get it working..  This thread has a 5-start rating on it and even though it hasn't been locked, has over 2300 views on it.. So I can't complain and glad to see that it's helping others as well..