The chinese symbol on the back of Jerry's robe means "Weak".
When the portal is activated in Brazil, a soldier runs up and lights it with a lighter, much like the Portals to the Nether in Minecraft need to be lit to be used. Minecraft is also heavily mentioned in this episode.
The President's genitals can be seen in explicit detail for a few frames while he's shrinking. This is the only instance of uncensored nudity in the entire show, likely due to an oversight from the censors.
Jerry references a date with Beth where they listened to The Milwaukee Symphony Orchestra perform the music of Alan Silvestri, most notably a song from the movie Volcano (1997). Keith David who voices The President in this episode was in Volcano.
When the president switches the TV off of Rick & Morty via infrared satellite to music, the screen shows Traci Jenkins and the Jenkenettes "Prisoner to my Emotions" already in progress.