Categorisation will certainly be error prone as there is so much similarity because fireworks and gunshots. The main difference I expect is the speed of the shockwave resulting in steeper spectrograms for gunshots. However, a steep spectrogram is essentially showing a large amount of high as well as low frequencies. The higher frequencies degrade very quickly over distance reducing the difference of a gunshot from a firework the more this degrades.

Not finding evidence is a different problem, it could be as simple as using a revolver rather than a semi-auto that ejects the cartridges.

In any case, it would be great to see independent testing of this problem by the sort of people in this forum and you can use the software I developed last year (https://github.com/hcfman/sbts-aru) to do so. That software sets the time on the Raspberry Pi to have less than 1 microsecond of error, which is more than enough for any validation efforts.