So I've been reading through the Denver missions trying to figure them out in time to run a game but I ran into one part I don't quite get on this mission. In the interest of keeping away spoilers however, I will be as specific as possible while trying to not mentio names or events:

Basically, the Debugging/Transition section of the scene at the Five-by-Five seems to not make sense when compared to Da Svidnaya Wyatt section at the end.

The former has "... left after speaking to" and the latter has "two gunshots." and a much more tense situation. I don't seem to be able to figure out how they are related sine they both seem to involve W at his house with M, but with dramatically different outcomes.

The "Da Svidanya Wyatt" scene is only for groups that accept Mikael's offer in "Never Go Home." If the smuggler escapes during the "Closing Time" scene, there is a different ending between Wyatt and Petrov. I can go into the full details if needed, but the scene happens "off-camera" so to speak, which is why it isn't included in the Mission. The short version is that the runners' choices have a direct impact on whether Wyatt lives or dies.

The Mission in a broad sense had four outcomes: Wyatt continues smuggling for the Casquilho, Wyatt begins smuggling for Petrov instead, Wyatt escapes Denver, Wyatt dies.

So... "Da Svidanya Wyatt" only happens if the 'runners snag Wyatt and bring him back? So even if they accepted in "Never Go Home" but missed him in "Closing Time", "Da Svidanya Wyatt" will never play?

As written, yes. If you as the GM want to run it differently, then by all means do so.