Web browsers do not know how to display media (audio and video). They rely on 3rd party programs or "plug-ins" to handle the media. SS, like all other HTML generators/editors, allows you to embed media on your page, but it is up to the visitor's to have his/her browser configured to handle the media.
Due to the wide variety of media formates, this can be quite a challenge for the web designer. How do you embed media so everyone can view it?
One way is to specify the player required to play the media. This is done in SS by choosing a specific media format using the Foreign Object Format type. Several common formats are available: QuickTime, RealAudio, Flash, and Shockwave. If the specific player is not available, you can provide a link to the required player; most media players are available as packages that can be downloaded and installed. If a browser plug-in is available, it will automatically install itself.
While the mp4 media format is common, there are very many different types of players that can be used for this file type. By not specifying a player, you are depending upon the visitor having a player pre-installed and configured to handle your file. As you have found out, this is not a very good option. Since Quicktime is capable of displaying mp4 media, try using that Format type in SS.
Another problem is your host needs to have your server configured to properly handle mp4 files. While most hosts are properly configured, some are not, and some choose not to because of the heavy bandwidth requirements of this type of file.
Have you considered uploading your file to YouTube, and then embedding the code for their player onto your page? This provides the benefit of embedding a player capable of playing your file, plus it moves the bandwidth overhead to their server and not yours.