Dr. Bellows has met Jeannie many other times including in the first season when she and Tony almost got married, in the second season when she worked as General Patterson's secretary and Dr. Bellows found out the CIA had no record of her, and in the third season when Amanda brought her home thinking she was Tony's mistreated wife and she stayed in their home. But here and leading up to the wedding, the Bellows act like they have never met her before and never question her previous engagements or "marriage" to Tony or the fact that the US government has no record of her.
Tony and Roger's breath is not visible in the freezing cold of the Aleutian Islands.