Could anything bad happen by having a confirmation e-mail sent to the wrong e-mail address?

No. Usually when I build registration sites, the user name and pword are not sent with the confirmation email to the registering party. Once you confirm your email, you are usually asked to log in. In some cases, the cookies on your own computer may save your user name and pword before confirmation and you can be automatically logged into your account the next time you visit. However, you always go through a security process. Either way, it would be impossible for someone else to access your account freely.