What precisely did this corruption consist of?  

"For all flesh had corrupted its way on the earth," they were all destroying their own seed.  They did not want to procreate and used sexual union for pleasure only.  This is what is meant by Yeshayahu 57:5, "the ones who slaughter the children."

Our Sages (Niddah 13) comment on this that they squeezed out their semen before impregnating their wives.  Seeing that they had become guilty of destroying semen which becomes a fetus after forty days, they were punished with a deluge which poured rain on them for forty days (Pirke de Rabbi Eliezer 22).

Actually, the people of that time were guilty of four sins:

1. idolatry
2. sexual licentiousness - including incest
3. murder
4. gratuitous violence.

The sin of corruption did not only include humans but it had also corrupted the behavior of the animals.  This is why our Sages (Sanhedrin 108) explained, "the ones who had become guilty of wasting hot semen were punished by a deluge of hot water."  This fact is based on the words used at the end of the deluge in 8:1 "vayashoku hamayim" (and the waters cooled off).