I’ll just give the link. One vice principal was fired for having an affair with a PTA mom. Another teacher at a different public school was fired for having an affair with a mother of one of the students at his school.
The story doesn’t tell how they were found out but from the tone of the story, my best guess was that they were seen together.
A few other bad teachers in Tokyo are also briefly mentioned.
Here’s a link to the story in Mainichi:
Tokyo Educators Sacked Over Affairs With Students’ Mothers