Bloodhounds (and all tracking dogs) find people by scent. So showing the dog a picture of Major Nelson was pointless, the dog would not be able to find him unless they gave him something of Major Nelson's to smell which they easily could have done instead.
It's not a normal bloodhound. It's a magical bloodhound.
It's not a normal bloodhound. It's a magical bloodhound.
After he switches bodies with Roger, Tony tells Jeannie's bloodhound that he is in Major Nelson's body. He should have said Major Healey's body.
Near the end, when Gen. Peterson and Dr. Bellows arrive at his office, the nameplate says Maj. Healy. But the credits always spell it Healey. (This is common throughout the series; the prop department often spelled it Healy despite the spelling of Healey in every credit of every show.)
At the 4 minute mark (syndicated version), both Barbara Eden and the dubbed voice of Larry Hagman each flub a line but recover quickly.
When Roger ran into Amanda Bellows (when he was in Tony's body) and she questioned who he really was, at the very least he should have been able to realize that he wasn't wearing the right uniform! He wore a green Army uniform and Tony wore a blue Air Force uniform. Even without a mirror, he should have been able to tell that something wasn't right.