How many Jews were there at exodus? According to Gen 46:27, Jacob entered Egypt with a family of 70. Kohath was Levi's son, Amram Kohath's, and Moses Amram's, so Moses's generation was 2 generations from Kohath's. 600,000 men, with women and children, left at exodus (Ex 12:37).

Meanwhile, before Moses was born, pharaoh ordered, that all male children from then on have to be killed. Moses survived miraculously, so 600,000 has to refer to men from generation above. Roughly estimating, 35 women (half of 70 that entered Egypt), gave birth to 1,200,000 people, which gives a fertility rate of about 34,285 (assuming 0 mortality). This seems quite large.
Moreover, if we assume that Jews didn't stop procreating with pharaoh's command, at that fertility rate, there would be about 20 billion women in Moses's generation.

Further, despite lacking partners from same generation, they could be impregnated by their uncles (Moses's mother was the aunt of his father, so it probably wasn't that uncommon), which would push the number even further.

Such numbers are very unlikely, and since Bible is inerrant, can you help me find error in my reasoning?
There are two things you're missing:


The time from Jacob's arrival in Egypt to the nation's liberation under Moses was roughly 400 years.
It is a common (but often missed and misunderstood) practice in biblical genealogies to "telescope" the list of names, focusing only on key individuals in the list.  (Going along with this, the word translated as "father" can mean a person's actual parent, or it can mean a more distant ancestor.)


Referring to this source for example, the article states the following concerning the period of time you're looking at:


  In the Old Testament period, it was important for every Jew to be able
  to trace his lineage back to prove his tribal affiliation—it was even
  more important for Levites and the descendants of Aaron in order to
  prove they were qualified to be priests (see Ezra 2:59–63). So we can
  see that in Moses’ day, he is said to be the descendant of Levi,
  Kohath, and Amram. This is supposed to cover a period of 400 years,
  and we’re given enough generations to cover just about ¼ of that.
  That’s not a problem however; the genealogy isn’t concerned with
  giving an exhaustive list of ancestors; just enough to tell us where
  Moses comes from. So we have Levi and his son, along with Moses’
  father.


So as Cerulean Chelonii noted, the four centuries between Jacob and Moses was plenty of time to allow the population to reach the numbers given at their first census.