Shortcomings of GA site overlay: http://www.lunametrics.com/blog/2009/03/17/site-overlay-issues-google-analytics/ It counts pageviews, not clicks on particular links, according to this blogger.
Alternatives: http://www.lunametrics.com/blog/2009/03/27/alternatives-site-overlay/ Some services offer detailed click analysis, but they’re not free.
BioMed 2.0 
Looks like the only issue is for links going to the same page. No? And in that case, the data you get shows total clicks to that page.
Right – so site overlay is not a tool to find out which links people are clicking on, when there are multiple ways to navigate to a page. Question is, do we want such a tool?
Maybe it makes sense to see how we might use site overlay on our site(e.g. on the homepage) and see whether there are many ways to get to the same next critical pages or not. E.g. can we use site overlay to see if people click on any of the individual news and events titles vs. the profiled events & deadlines? Or, whether we can tell which of the ‘Get Help’ items gets clicked on the most?
More resources for data-driven design:
In the mean time, if you’re a designer and are intrigued about data and design, here are some resources you might find interesting:
– Follow KISSmetrics on Twitter for plenty of design, analytics and testing link goodness.
– Read the Marketing Experiments blog to see data-driven design in action.
– Dive in yourself right now and do a test with Google Website Optimizer
from http://design2-0.com/articles/in-defense-of-data-driven-design/?
A new analytics service called Chartbeat emphasizes realtime data: http://chartbeat.com/
To make Google Analytics Site Overlay properly display which link was clicked and not display all clicks to a page at the link, you need to make it aware of the location of the link. For example:
There is a link to mypage both in a block on the right sidebar and on the left sidebar on all nodes of http://www.yoursite.tld. You want to know, which of the two gets more clicks. To achieve this, you need to add a parameter link-id to the href: http://www.your-site.tld/mypage?linkid=leftsidebar and http://www.your-site.tld/mypage?linkid=rightsidebar.
This identifies the region the link is in for Google Analytics. You could also add &block=blockname or &nodeid=123 or a combination of them, depending on your analytical needs.