Using common slider in all sites

Do all your sub-sites use the same theme?
If they do, then the most light-weight solution would be for you to hard-code the slider in your template file.

This will give you the flexibility of doing whatever you want with your slides and the script you’re going to use, but at the same time it will mean that each time you want to change a slide you’ll have to dive into the files and correct that.
Usually that’s not really hard as changing a slide would simply mean changing the url of an image, a link and perhaps some text. It shouldn’t require more than 5 minutes.

If you use different themes on each site then you could create a php file on your wp-content folder (let’s call it slide.php ) and then from each theme simply do a

<?php include PATH_TO_SLIDE.PHP_HERE; ?>

This way you can change the code in one place and slide will change network-wide.

If you are looking for a solution that will allow you to use a plugin I’m afraid that I am not aware of any plugins that can do that job…

I hope that helps!