I get that, I really do. But it's not a BUG. It's a valid point. It's annoying. It's not a bug.
You're running an old browser (and an old OS), and you can't upgrade. That doesn't change the fact that they are, both, out of date and do NOT support things that Safari 5.1 (for example) does. Otherwise you'd have Safari 5.1 and not 5.0.6. (And don't get me started on the annoyance of OS's requiring you to upgrade hardware to upgrade software. Microsoft's just as bad.) You get this alert on any old OS with a non-latest browser (XP only goes to IE 8, which is out of date).
So the point I have is this: Your browser's old and not supported anymore past security fixes. It's not being actively developed, it won't get the new HTML5 whizzbangs. It's old and it may not work right on WP. WordPress is alerting you to this.
If you don't like it (and who would when they can't upgrade?) you can click the link that says 'Dismiss' and it'll go away. Or you can install this plugin: http://wordpress.org/extend/plugins/no-browser-nag/
Just remember to uninstall it when you do get that new computer.