Clicking Alerts marks them all read, and therefore a little useless. A small way around this however, in case others haven't figured it out, is to NOT click Alerts, but instead open the Your Account drop-down menu and click "Your notifications." You'll see all your alerts with starts next to them that represent new ones, and clicking each link (make sure you open it in a new window; I believe simply going to this page also marks all alerts as read) will allow you to go through your notifications and not miss any.
It's not a perfect system, and personally I think Alerts should be tied with you actually viewing the content otherwise it's a temporary list that disappears the moment you look at it (This letter will self destruct in 5 seconds).
Some may have already figured this out, but for those who didn't I thought this bit of advice might help if you're bogged down by a lot of alerts when logging in the first time of the day.
* Oh gawd I hope not... if you are, I'm so sorry. :p