At the beginning, Koskov is questioning Bond about the sniper Bond disarmed (Kara). Only later in the film do we realize that he was trying to see if Kara had been eliminated to avoid revealing the truth about the "extraction".
Bond is also notably curt in cutting off Koskov's line of questioning, giving an answer that essentially lets Koskov draw his own conclusions ("I'd rather not talk about it."). Having clocked that the sniper wasn't a professional, he's got some early suspicions that all might not be as it seems with Koskov's defection.
Whitaker is said to be a failed student of West Point and a strategic moron, but within his mansion, there are a number of generals... including Adolf Hitler, a man who made a number of utterly stupid decisions during World War II and was also a huge slacker, preferring to go on daily movie marathons instead of actually running Germany. Whitaker looks up to him; no wonder he's a failure.