They struggled with many things, often time the minutiae of accomplishing something conceptually rather simple. For example, making an explosive with a significantly slower detonation velocity turned out to be very tricky. The concept was simple -- just add some barium nitrate to the TNT. But if you just did that, the mixture stopped flowing nicely, and it still was either not slow enough, or refused to explode at all. Extreme technological nuances were required just to prepare a mixture of two simple ingredients before satisfactory results were obtained. This one thing was its own research project.
Accurately casting explosive in odd shapes, without different ingredients separating, and without producing voids when the melt solidified, required developing a whole new technology with careful gradients of temperature in the molds.
They tried lots of different commercial and handmade detonators to find which ones would work most consistently. That took an awful lot of time.
The electronics itself was probably least difficult -- a microsecond was already a very long time for the electronic circuits even in 1945. One could use an off the shelf oscilloscope to see if the detonators worked simultaneously or not. Incidentally, 2/3 of the cables in the famous picture of the "Gadget" are not the detonators, but the simultaneity sensors -- reporting the difference between the earliest and the latest detonation fronts.
Everything was tested extremely extensively. Tremendous resources were spent on testing and test equipment. All in all somewhere between 20000 and 40000 explosive tests were performed at Los Alamos during the project.
It is not often emphasized how much of the work was done in the explosives laboratory in Pittsburgh before passing it on to Los Alamos. They have developed the slow explosive. They also reproduced from the earlier British work and further developed and tested the concept of the lenses, together with many other more advanced things which did not find an immediate application in the bomb. The director of the laboratory, George Kistyakowsky, took over the explosives work at Los Alamos, once the implosion became the main focus of the project.