The artifacts you refer to appear to be present when playing the games on physical Nintendo 64 consoles.
There is nothing wrong with the emulator; it is simply doing its job.
To answer this question, I simply went and looked at other playthroughs of the games.
First, we have "Super Mario 64". This was an easy one to find - I just looked up a "Games Done Quick" video to find a version being played on the Super Nintendo 64. I can clearly see the same dark polygons drawn around the edge of Mario's feet. I note that they are not always seen - I notice they disappear in the water level. I assume the polygons are being drawn that way based off the lighting, but in the example scene you show, the original console draws them in the same way.
Secondly, we have "Mario Golf 64". I found it impossible to find a verified playthrough of this on an actual Nintendo 64 console, let alone specifically as the character Charlie shown in the original screenshot. However, literally everywhere I go, screenshots with Charlie as the main character show the exact same overlapping polygons. I assume this was simply a developer error.