The jQurey autocomplete plugin on this site is going to be part of jQuery UI. If you’re interested in contributing to that effort, here is an introduction with the most important resources.
To start, take a look at the Planning Wiki Frontpage. There the autocomplete widget is listed with a high priority. That means that the widget gets a lot of focus from the team for the next releases. From there we can get to the planning page for the widget itself. It has an informal description of the expected functionality, along with links to related resources; some visual designs; a more formal specification as well as recommendations for base and transformed markup. The latter describes the markup that the use of the widget has to provide in order to use the plugin, the latter describes what results after the widget did its work. Overall, the specification describes the current state of the widget, which leaves still a lot of work.
The code itself can be found as a branch in jQuery UI’s subversion project. This is a branch of the current trunk, which makes merging changes from trunk to the branch, and later from the back to trunk easy, but has the disadvantage of always listing all the other stuff.
So, if you’re still interested, the Planning Wiki also describes in detail how to get involved with the project. If you have specific questions, or just want to introduce yourself, join the jquery-ui-dev Google Groups list.
If you want to start fixing bugs, the existing tickets for the autocomplete widget are in the bug tracker.