No, there is nothing wrong with it. People are not likely to be able to figure out that there is any relationship, and if the great great uncle is from the "other side" of your grandchild's family, he is not related to you at all.
He would be his great great great uncle
Your great uncle's grandchild is your second cousin.
You and your uncle's great grandchild are first cousin, twice removed.
Your great-great-great uncle's great-great grandchild is your third cousin, once removed.
She would be your first cousin, once removed.
Your uncle is your child's great uncle and your grandchild's great great uncle. Your grandson is your uncles great great nephew.
Great aunt or great uncle depending on your gender.
Great grandniece or great grandnephew
Your grandfather's brother is your great uncle. The wife of your great uncle is your great aunt.
Your second cousin, twice removed, is the grandchild of your second cousin (the great great grandchild of your great aunt or great uncle) or the second cousin of your grandparent.
Your Great-Uncle is your father's uncle or your mother's uncle. Another way to look at it is to realize that your great uncle is the brother of one of your grandparents.
Your great uncle's grandchild is your second cousin. (Your great uncle's child is your first cousin, once removed and your parent's first cousin.)