Karma-45 & Volk: Mission: Black Sky. At the start, on the first two enemies you down (who jump your ship).
KBAR-32: Mission: Black Sky. After Salter gives you grenades when you go through a gate (and end up in a large town square), look on the ground of the streets to find this weapon.
EMC pistol: Mission: Black Sky. Shoot enemy soldiers in their legs. When they're on the ground, crouching and firing at you with their pistol, defeat them and collect their weapon from them.
F-SPAR Torch: Mission: Operation Port Armor (Civilian Terminal). Defeat the second strong/alternative type bot, which drops this weapon. (The first one dropped a shield).
Mauler & Reaver: Mission: Operation Port Armor (Civilian Terminal). In the armory, which you are forced to visit. Be sure to collect both weapons inside.
Type-2: Mission: Operation Port Armor (Boarding Party). When going through the dark hallway, keep checking your right side for an armory door to your right. The Type-2 can spawn there (randomly).
R3K & DCM-8: Mission: Operation Taken Dagger. When blasting the ship open at the beginning, search the left side of this first room to find both weapons in a cabinet.
P-LAW: Mission: Operation Taken Dagger. Found at the end of this mission, inside the armory in the last area.
HVR: Mission: Operation Phoenix. Dropped randomly by enemies in space.
RPR EVO & Eraser: Mission: Operation Deep Execute. Found in the missile assembly hall, immediately to your right upon entering. The missile assembly is where you must locate a tech officer upstairs. Before doing this, enter the armory first.
Ballista EM3: Mission: Operation D-Con. Relatively early on in the mission, go through the redly lit hall with flames and turn left when you first can to find the armory in which this weapon can be found.
Spartan SA3: Mission: Operation Burn Water. Found right before fighting the enemy mech.
Banshee: Mission: Operation Black Flag. Randomly dropped by enemies at the early start of this mission, when you're chasing the prisoner. It can also be found in the armory during Operation Burn Water (see video).
KBS Longbow: Mission: Operation Black Flag. If you didn't find this in the armory during Operation Burn Water, then you can find it at a fixed position during Black Flag. It's at the shop, just outside, when you meet heavy resistance while you're chasing the prisoner. It can be found against the outer shop wall. Kill your enemies in the distance first. (Alternatively you can find it in the armory during Operation Burn Water, see video.)
Oni (handgun), Erad, Titan Scout: Mission: Operation Black Flag. Near the end of the mission, when you land on the enemy ship and Salter (and various other soldiers) come to your aid, look for these three weapons on the left side of the area. They have fixed positions, so they're always there - good to know.