[Adm.Lee]

The April '11 issue of Naval History had an article, "Cold War duty in the Black Sea Fleet" by Vladimir Mandel. He served as a junior officer on the Kashin-class DD Komosomolets Ukrainy in 1969-72. He said, "Of the political team on board the ship, the KGB man was the only one possessing the qualities of a good officer."
"Three such officers were in our ship"-- each from different departments, but all were there for political indoctrination, which the crew found boring. He thought the Navy had less political indoctrination than most servicemen.
"Even so, the political officers were unpopular, for they produced unnecessary paperwork and harassed the crew with boring, time-wasting activities: political discussions, the study of Lenin, and perhaps most annoying, specially prepared propaganda from the media-- rudimentary Marxist ideology that generally was poorly written and intellectually insulting to any reasonably educated man."
When the ship transited the Black Sea Strait, the Deputy Commander for Political Affairs did not allow anyone on the weather deck, and stood guard with a pistol and grenade, to keep any from defecting. This, of course, undermined the propaganda about the decadent West and its "atrocious fangs," which was noted by the generally well-educated crew.

From that picture, I'd say the political officers would likely by bureaucratic drones, without much authority. In wartime, they'd quickly drop to a position like the chaplain and/or morale officer, unless they have worthwhile training and/or leadership qualities. By the time of 2000, I'd easily see them get absorbed into the office corps at large, and either put to real work, or shuffled aside-- like manning MP posts or running convoys, just ready for American stragglers to pick off.
The KGB guys, on the other hand, who have been monitoring for signs of desertion and treason and defection, are probably pretty good at their jobs by now.