They were definitely afraid they would not detonate correctly, and calculated that even if nothing went mechanically or electronically wrong there was a great than 10% that it still wouldn't work very well. The plutonium bomb in particular was an immensely complicated device electronically and could have failed if any of those components failed. As a result there was a high degree of redundancy in its wiring (technically the bomb attempted to arm and fire itself twice simultaneously at the same time).

They were also afraid of the bombs detonating prematurely. In the case of the uranium bomb this meant leaving out a key component until they were already in the air. In both bombs it meant having people go back and arm the bombs electrically by removing safing plugs.

I am doing an AMA here on the Manhattan Project next week, if you are looking for more interesting information.

I would think the greatest worry is a complete failure involving the plutonium bomb.

Although the Japanese would have not known it in advance, they could have powdered it and sent it via balloon to the US west coast as they had done with conventional explosives in the previous months.

" calculations show that one pound of plutonium could kill no more than 2 million people by inhalation. This makes the toxicity of plutonium roughly equivalent with that of nerve gas."

But unlike nerve gas, the dust will settle in a wide dispersion at ground level. A very dangerous thing for the USA to plop down in the middle of Nagasaki and have Japanese scientists take to a laboratory.