I recall reading at some point that there were fears regarding the power of the explosions: eg: the atmosphere would ignite or the chain reaction would not stop, etc.
While it seems like scientists performed due diligence with assessing these concerns via modelling and research, were there any concerns or dangers that remained truly unknown until the test was performed?
How did they determine proper range/distance for safety, eye protection, etc-- or was that all just protocol for any experiment of that size and estimated power?
They made assumptions about the likely explosive effects and the largest hypothetical effects, and planned around those. They also did extensive small-scale experimentation to help them anticipate the results.
Every kilogram of plutonium that fissions releases around 18 kilotons of energy. The amount that fissions depends on the amount of fuel in the bomb and the bomb's efficiency. The scientists estimated that the maximum likely yield was around 5 kilotons. They were wrong on that -- it was more like 20 kilotons -- but from an effects standpoint the difference is a small one. Nuclear weapon damage does not scale linearly, it scales as a cubic root. So to double the damage you have to increase the yield by a factor of 8.
The total plutonium in the bomb was 6.2 kilograms, so the total theoretical yield was around 110 kilotons. Their nearest bunkers were well outside the radius of significant effects for even the most optimistic bombs.
All that being said, they tried to be very conservative on safety and recognize that there were many unknowns. They stationed people in towns around the site with Geiger counters, ready to evacuate people if the cloud drifted or lingerd in populated places.
You may find this essay I wrote last summer for the 70th anniversary of interest. It tries, among other things, to reconstruct the uncertainties and unknowns a bit.