In "A Loaf of Bread, A Jug of Wine and Peaches", Martin falls in love with a stripper named Peaches Ancream but apparently remains oblivious to both what a stripper actually does and to the numerous innuendos thrown around in that episode. This in spite of Tim explaining to him what her job was, and Martin being both a mind reader and an expert on Earth. Rule of Funny was in effect, but Martin has scolded Tim for his dirty thoughts many times, so it's a little hard to believe that he was not only unaware of the situation but remained so throughout the entire episode.
Martin's powers have been shown to include the ability to change people's minds telepathically. It doesn't always work, but there are many situations where this would have come in handy when he doesn't even attempt it.
The Film
Fridge Horror
The Veenox 7 Nerplex, full stop. It seems that unlike most of the other Nerplex, whoever uses it doesn't simply transform to "look" like the native alien. Their personality appears to be almost completely overwritten. For example, the normally sweet and shy Lizzie doesn't hesitate to viciously murder the SETI guards attacking Tim in order to rescue him. This actually makes sense, do to Martin's previous warnings about the Veenox 7 Nerplex.
