While I like "Field of Fire"(DSN7), it is an odd episode. This is the one where Ezri wields a TR-116 that fires tritanium bullets that are beamed into a room and shoots a loony Vulcan murderer.
The main issues I have relate to the logic and continuity of the episode.
For instance, when a tool went missing in "In the Hands of the Prophets"(DSN1), O'Brien scanned for independent tritanium sources on the station, which worked quite well. Yet here, when they are dealing with chemically propelled tritanium bullets, nobody looks for them. It is possible that in wartime there were lots of such sources or some dampening field in place, but still. Certainly there was nothing to suggest any sort of dampening field being used by the murderous Vulcan ... the extent of his security seemed to be a blanket wrapped over the gun.
Speaking of chemical propulsion, we never hear of anyone scanning the bullet to try to get residue traces and then scan for either the combustion products or the actual 'gunpowder'. In "Hollow Pursuits"(TNG3), a Federation starship can be easily scanned for any of a number of materials. Yet here, the extent of the science seems to be Odo's discussion of powder burns.
Sure, the transporter that beamed the bullet may have exclusively beamed the tritanium, but still.
Everyone accepts Odo's 20th-Century-crime-novel-based theory of powder burns, as well, yet there is no reason to believe that the gunpowder employed would've suffered from such inefficient combustion as we have now. When making a new projectile weapon in the 24th Century with a simple chemical propulsion for use in low-tech-only environments, a wide variety of different concepts could have been employed. Even today nanotechnology is being employed to greatly enhance explosive yields by driving up the combustion fraction, making more use of what was there. And yet, in a time where (as seen, for instance, in the long list from "Night Terrors"(TNG4)) myriad possibilities exist for making things go boom, we are to believe that there would've been powder burns all over the body? It makes little sense.
And, of course, it seems as if Ezri is the only one investigating, but that's neither here nor there.
In short, it was a good romp in Dax's mind, but beyond that it was quite perplexing. Maybe things would've gone better if they'd still had a science officer active among the senior staff.