Well, let's see where the passage of time and repeat viewings land this film. Other criticisms have since occured to me, but I'll pass over them in silence - for now.
The monologue is good (albeit on the nose). I think the segment you mentioned about The Godfather and so forth is clearly playing on gender-based stereotypes, and I didn't personally find it annoying. That said, I know several women who were infuriated by The Godfather being used in that way (ie stereotyped as purely a film for men) so perhaps your feelings of being "triggered" aren't entirely without precedent. :)
Elsewhere, I'm aware of men foaming at the mouth because all the male characters here are dimwits, but personally I just found that funny, and even a bit refreshing, since there have been many films (not necessarily bad ones either) where the female characters are all dimwits. Time the shoe was on the other foot. :)