I was trying to use the Current User webpart in an ASPX template and I noticed that setting ShowUserFullName="false" wasn't working, so I looked inside CMSWebParts\Membership\currentuser.aspx.cs.

In the setters for ShowLabelText, ShowUserFullName, ShowUserName, AuthenticatedLinkUrl, and PublicLinkUrl, there is a space before the end quote of the string that is the property name, which makes the setter fail.

For example:
this.SetValue("ShowUserFullName ", value);

I changed this to:
this.SetValue("ShowUserFullName", value);

And now it works as expected.