Hi Ken,
This most likely has to do with the way the Javascript is loading on your page. You have 2 instances of Jquery loading in the head. One of the instances is after the simpletweet
js. This means it is re initializing jquery after the tweet
js and therefore can not run the script to fetch the tweets.
This is evident by the error
$(".simpletweet").tweet is not a function
Take a look at this screenshot of your source
http://www.joomlajunkie.com/images/snaps/jq-ea.png
Notice how its re initializing jquery after the simpletweet
js is called. Try disable the second instance of jquery from wherever its getting added and it should fix it.
The tweet module is working fine I tested it on 5 different installs now and they all work.