"Yeah, the river runs red down the legs of a city."

In my opinion this is an explicit reference to the rupturing of a young woman's hymen. In the book, 'No One Here Gets Out Alive', it is mentioned that he frequently had sex with young women. Presumably the cities and towns he mentions in the song refer to places he has actually been while touring with the Doors. It is a straight forward assumption that he had sex with numerous groupies, who being very young were probably virgins. Doubtless, he over exaggerates the enormous quantity of bleeding he caused, but nevertheless it probably reflects his own personal sexual experiences. Moreover, he also appears to express some remorse for his actions.

"Blood in the streets runs a river of sadness."
"The women are crying red rivers of weepin"

There may be another sexual reference.

"She came"

This line is repeated numerous times throughout the song. It's more debatable as to whether or not one of his sexual encounters actually ejaculated. Although it is clear that women have hymen and that these often do rupture and bleed during sex, there is no scientific basis for the notion that women can ejaculate during sex. They simply do not have a secretory organ that serves this purpose. Nevertheless, it is a common belief that they do, and this suggestion may also have been intentional.

Two other lines worth mentioning.

"Indians scattered on dawn's highway bleeding.
Ghosts crowd the young child's fragile eggshell mind."

According to the biography, Jim Morrison witnessed a terrible automobile accident when he was still a boy. A truck carrying native American Indians overturned, and he saw them lying on the road bleeding. According to his own account, he felt that the Indian's ghosts were trying to enter his mind. Perhaps feeling some remorse for his sexual misconduct, Morrison suggests that his actions may not be his fault, as spirits possessing him may have provoked his actions.