Louis Slotin was a real person and the story told about him and his death from radiation is mostly true.
When Charlie is writing probability numbers on the board he writes 1 then the next number is 1.0. That is an error. They are the same thing/number. (Edit: there is a difference mathematically as 1 is a number rounded to the ones place and 1.0 is rounded to the tenths place, meaning the true answer is probably slightly higher than one. Also, visually, 1 and then 1.0 reflects the episode number (1x10).)
Season 1, episode 10 -- all the numbers in the opening are divisible by 10 (500g, 20kg, 400 threats) except 1 (1 dirty bomb).