Two rooms are behind this gate, at either end of a short hall. One room contains a large stone chest and some Dwarven Oil, as well as a few miscellaneous Falmercraft items. The other room holds another vial of Dwarven Oil, a small stone chest, and an entire suit of Falmer armor. If you haven’t got much in the way of good light armor by now, the Falmer armor may be worthwhile. Keep in mind, though, that you need chaurus chitin to refine it into stronger forms, and down here you haven’t seen very many chaurus. It may turn out not to be worthwhile to pick it up, as you have been through rather a lot of dungeon, collecting Dwemer metal to smelt into ingots and are likely looking at a rather full inventory.
Once you’ve taken the valuables you desire from up here, return to the bottom of the tower and you can ascend the stairs and pass through the large gate.
All that waits you in this secondary courtyard are two Falmer- but one of them is a Falmer Shadowmaster, a deadly melee warrior who fights with blade and shield. You will need help from your follower to deal with the Shadowmaster, although the other Falmer is negligible by comparison. It can be well to your advantage to use the terrain in the area in whatever way you can- there are several slopes and objects you can jump atop that the Shadowmaster cannot climb, so you can use this to strike with ranged attacks from out of its reach. Alternately, by fighting your way up the stairs and then hopping down off of them, you can give yourself repeated mid-battle breaks as the Shadowmaster runs the staircase to catch back up to you.
Once the two Falmer are dead, ignore their huts- nothing of value is in there. Instead, look to the door in the stone alcove that faces the open gate leading onward from the courtyard. The locked door conceals what can only be a Dwemer workshop- a half-disassembled Dwarven Centurion lies on the table here, and you can take a number of useful pieces of Dwemer scrap from the table around it, as well as many very nice pieces of its workings from within the massive armored form.
Proceeding on through the gate brings you to a large ramp, at the bottom of which lie the remains of a Falmer, a Dwarven Sphere Guardian, and a Dwarven Spider Worker. Loot them and then ascend the ramp to find one last Falmer corpse before the large door that leads to the last chamber of the dungeon, which is afforded its own entire location- Mzinchaleft Gatehouse. This is where you really need to be prepared: tired, of full inventory, and drained of some or all of your resources you may be, you have one more obstacle to take on before you are done in Mzinchaleft.