I don't know if this is the workaround I have heard mention, but what I have found is if you are super quick and click on the dialouge box before it dissapears (and it only appears for a spit second) the mission log WILL update allowing you completion. (I can confirm that it worked for me after 5 failures)
So it seems the "break" or problem with this mission ISNT the mission log not updating, the problem is the dialouge box from your Bridge officer instantly dissapearing that it the bit thats broken.
I am happy to confirm the above dose work as I was eventualy able to complete it by hiting F as soon as the dialouge box appeared.
In addition, I beamed up to my ship hoping I could just make the map reset only to discover it took me back to Qo'nos with no "continue" popup... so I had to drop the mission entirely. I hope this gets fixed soon as it's a serious setback to leveling my KDF toon (i want to do the story missions in proper order).
I finally found that if you travel to the Gorath system, can you resume the ground part. However, I tried it again and still same bug as before.
However, I aborted the mission, flew to Gorath from Qo'nos (took a while, might have reseted the map?), re-entered the "Sulfur My Wraith" mission stage and re-did the mission up to the Evidence. I don't know if it makes any difference, but this time I used the mouse to interact with the container (on a previous attempt, I used the 'f' key) and I was able to click "Continue" (?) on the following dialogue before the container was transported out. This time, the mission objective was correctly updated and I was able to finish the mission successfully.
While this workaround may help you to finish the mission, the bug does need to be fixed, it sticks out like a sore thumb in otherwise immersive mission flow.
Yep, this works, select the cargo with mouse, keep mouse centered in screen and click like a coked-up spider monkey.