I just played through "Doomsday Device" and was unable to reproduce this issue.
It sounds like the main mission is not advancing properly at some point even though one is still able to move on and continue playing.
For those of you experiencing this issue, try to pay attention to your Mission Trackers. There are two that display in the game. The Main Mission Tracker which is always present by default below your mini-map, displays the main mission and its stages. Then there's the Open Mission Tracker which appears below the Main by default, which displays the individual map mission stages. In general, the Title displayed in the Open Mission Tracker should sync up with the mission stage displayed in the Main Mission Tracker.
For example, when one first arrives in the transporter room of the Targ, the Main Mission Tracker lists "The Doomsday Device" with "Boarding Party" below that, and the Open Mission Tracker displays "Boarding Party" as the Heading with "Secure the Engineering Deck" below that. When all the steps on the Targ are completed, the listing below "The Doomsday Device" changes to "Silent Running" with "Go To Imaga System" below that. When one arrives in Imaga, the Open Mision Tracker heading is now "Silent Running" which matches the Main Mission Tracker.
So what you want to look for is a situation when the line below "The Doomsday Device" does not sync up with the Heading of the Open Mission Tracker, especially after a map transition occurs. Such as if one arrived in Imaga and the Main Mission Tracker still had "Boarding Party" listed below "The Doomsday Device" instead of "Silent Running."
Why am I telling you all of this? This issue doesn't happen every time one plays the mission and I just don't have the time to play through this mission over and over again to try and find where it is breaking. Therefore, I need your help to track this down. If you folks can find the point(s) where the mission is getting out of sync, and especially if you can remember what you were doing just before it happened, that will help greatly to track down the exact point where the mission is breaking, which is necessary to be able to fix it.
Thanks in advance for any assistance you can provide.