Let's see a couple of things.
First of all, don't worry you will not have any trouble of compatibility issues with WP 3.5 and WP Analytics Tracking.
The main purpose of this plugin is to let you easily add any HTML code you want on all your pages. So it's perfectly designed to add the Google Analytics Tracking code.
I know a solution to track the click on a single link with Google Analytics. Basically, here is the idea :
1- Create an event in your Google Analytics interface
2- Get the ID of this event
3- On your WordPress page (or post), use the editor in HTML mode (tab on the upper right hand corner).
3- Add for example this following code for one link (adapt the URL with the URL of your choice) :
<button onclick="window.open('http://www.google.com/');_gaq.push(['_trackEvent', 'nbr-clic', 'click-button1']);">link</button>
I haven't tried it, but you may also try this code :
<a href="http://www.google.com/" onclick="_gaq.push(['_trackEvent', 'nbr-clic', 'click-button1']);">link</button>
This code is a "normal" link. But I don't know if the Google Analytics event is properly triggered.
I don't think it is possible to automatise this process for all your link.
Hope this answer helped you.