In worst case scenarios, there are stories of these children coming back to insert themselves uninvited into the lives of the donor. This might work out or it might destroy a carefully built family life. In addition, while it is rare, it has happened that biologically related children have hooked up in sexual relationships that socially and genetically are not acceptable.
As with Posts 3 and 4, I think that having a bunch of "your" children out there that you didn't know about might be a bit problematic. But going one step beyond that, it seems to me that if you donate sperm and then go on to have a family of your own, things might get a little bit difficult. It might bother your wife and/or children that there are these other kids of "yours" running around out there.
I think the fact that you have "fathered" children and have no idea who they are or what they are like. At the time of the donation this may not seem important but I would think eventually you would get curious.
Another problem that could possibly happen is that the sperm donor may want to someday know the children that he fathered. I believe that this is unlikely but still possible. As the previous responder said, there are numerous confidentiality contracts (for everyone) that need to be agreed to but later in life the donor may have a change of heart and want to know who his biological children are.
An argument could be made that sperm donors face an ethical dilemma, in that if their sperm is used to father a child, or in many cases, several children, then do those children have any right to know who their father was? Most laws regarding this issue have created sealed records that would not reveal the identity of the donor unless they gave their permission, and in order to use a sperm donor, the women who pay for the service have to sign a waiver to any legal action seeking to identify the donor by name.
Some would say that the children of donors should have the right to find out the current medical profile of their biological father in order to better care for their own health.