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The replisome makes a mistake about once in every 100 million bases incorporated. This is an error rate of 10-8. The repair mechanism fixes 99% of these errors for an overall mutation rate of 10-10. http://sandwalk.blogspot.com.au/2010/11/human-mutation-rates.html
It is certainly possible for a fetus to develop a cancer, if enough of these mutations disable the critical genes. A cluster of mutations like this could occur in a single cell due to normal rates mutation during cell division up to birth, but it is fairly unlikely.
[Sacrococcygeal teratoma] is seen in 1 in every 35,000 live births, and is the most common tumor presenting in newborn humans.