Undifferentiated stem cells could produce tumors and multiply unchecked within a patient, causing more problems than providing appropriate therapy. According to a recent article ion the New England Journal of Medicine:
"There are still many hurdles to clear before embryonic stem cells can be used therapeutically. For example, because undifferentiated embryonic stem cells can form tumors after transplantation in histocompatible animals, it is important to determine an appropriate state of differentiation before transplantation. Differentiation protocols for many cell types have yet to be established. Targeting the differentiated cells to the appropriate organ and the appropriate part of the organ is also a challenge.”
Harvard scientists reported in the Proceedings of the National Academy of Sciences that five out of the 19 mice injected with embryonic stem cells developed tumors and died." ˛
Stem cell lines will suffer the same tissue rejection problems as adult transplants. Once differentiated, these cells will express the HLA tissue antigens programmed by their parental DNA. These antigens must match those of the recipient or else tissue rejection will occur. An admission of the problem of immune rejection can be found from The Scientist:
"Within the [embryonic stem cell] research community, realism has overtaken early euphoria as scientists realize the difficulty of harnessing ESCs safely and effectively for clinical applications. After earlier papers in 2000 and 2001 identified some possibilities, research continued to highlight the tasks that lie ahead in steering cell differentiation and avoiding side effects, such as immune rejection and tumorigenesis.” ą

References
ą E. Phimister and J. Drazen. 2004. Two Fillips for Human Embryonic Stem Cells.” New England Journal of Medicine 350: 1351-1352.
˛ Bjorklund, L. M., R. Sanchez-Pernaute, et al. 2002 "Embryonic stem cells develop into functional dopaminergic neurons after transplantation in a Parkinson rat model." Proceedings of the National Academy of Sciences 99: 2344-2349.
Hunter, Philip. 2003. Differentiating Hope from Embryonic Stem Cells. The Scientist 17: 31.