I expect this will unfold slowly - not in the next episode, but over time as the war becomes relevant, or Dr. M'Benga's PTSD becomes an issue, or something.
I didn't come away thinking it was side-effect free. It looks like it came with high aggression levels that make it very difficult to control violent behavior. When they took it, they had a very good use for that violent behavior. In other contexts, it would probably be a notable unwanted side effect, like a rage in which the user stops being able to tell friend from foe.
It would be super-easy to note that the thing probably has major impacts on the human adrenal system in the long term. In the middle of a life-or-death situation, that can be acceptable, where long term use will probably kill you, make your heart explode, break blood vessels in your brain, and such.
Also, look forward to it already being illegal in civilian use, or even use by Starfleet personnel in peacetime. The Doc carries it around... but probably isn't supposed to.