TV was low-tech. Private inventors were working on improvements.
And he hadn't taken a new photo since leaving Germany.
What the what? These days, when this kind of thing happens, it can usually be chalked up to a set designer's intern who played it loose with a Google image search, but this was 1971. They had to walk all the way to the ... photo library, we guess? It's safe to assume they knew exactly what they were doing.
According to the film's director, Mel Stuart, the photo was a joke that fell flat, presumably because they (slightly) overestimated the number of children in the audience who possessed an encyclopedic knowledge of obscure World War II villains.
And an encyclopedic knowledge of dick slang ... but that's a whole other story.
Bormann was killed by the Red Army as he tried to flee Berlin, but there was a rumor that he actually escaped and fled to Paraguay, hence the reference about him winning the ticket in South America. Stuart went on to elaborate on the failure of such an obvious knee-slapper: "25 years after World War II, very few people knew or cared who Martin Bormann was, so the scene was never as successful as I had hoped."