Are there any ethical issues?

Are there any ethical implications with the collection and use of stem cells from umbilical cord blood?
No 

There is however some confusion between embryonic stem cells and umbilical stem cells, but the sources are entirely different.

The umbilical cord blood is normally discarded at birth and collection of blood from it poses no ethical or moral dilemma.

For more information about the main 5 types of stem cells, click here.