The CSS for borders needs to be rewritten so that the borders are rendered consistently for all browsers.
This fix can be tested by clicking through every generated page for dashboard, profile, and a test site in SO. This should be done for ie7, ie8, ie9, chrome, firefox, and safari, checking to see that the borders are render consistently. This process should be done for both ee-6.1.x and 6.1.x (CE).
Closing ticket per Evan's comment. We'll be on the look out for this periodically. Thanks!