I'm no internet whiz, but I'm assuming they updated something that is clashing with stored cookies. I was having the problem for the past two weeks and couldn't figure out how to clear cookies in all of my browsers (I use Chrome and IE at work and Mozilla at home).
Once I cleared my cookies, I have had no problems. I thought the site was getting mad at me for logging into my registry so much. :)
The only thing that Target can really do is put a message on their site saying to clear your cookies.