It's not technically wrong. I think function of that
you are referring to is that of a noun clause as explaineddescribed on this page under §5. ButHowever, to me it tends to sound a bit odd if somebody does this consistently.
I'm Dutch and in Dutch the usage of the word thatthat
in cases like these is very common. So this is one of the telltale signs somebody isof a fellow native Dutchman speaking english:).
Disclaimer: I sometimes find, I tend to think anything that sounds Dutch isn't proper English. So I might be slightly biased on this one:).