The next time you attempt to watch an archived game, you will get a dialog box saying "Safari can't display content on this page ... some content on this page requires an Internet plug-in that Safari doesn't support. The application 'Windows Media Player' may be able to display this content. Would you like to try?" Just click OK, and Windows Media Player will launch, and you will be able to use full screen mode.
I decided to post this here because mlb.tv seems incapable of providing this simple workaround, and I get lots of traffic to my blog from frustrated Mac users.
[robg adds: I can't test this one (mlb.tv is a subscription site), but it makes sense in theory.]

