When characters are confused or dumbfounded, their lips droop down their faces. This is an homage to The Ren and Stimpy Show, in which Ren would do the same thing.
Rick's catchphrase "Wubba Lubba Dub-Dub" was accidentally conceived by series creator Justin Roiland who also voices Rick. While doing a recording, a scene was described in the script where Rick would be spinning around on the floor and yelling "Woob woob woob woob woob" like Curly from The Three Stooges. Roiland, who is dyslexic, misinterpreted the line and blurted out "Wubba Lubba Dub-Dub". The makers liked "Wubba Lubba Dub-Dub" so much that it stuck with them. They later decided that it means "I am in great pain. Please help me".
In an episode where Rick and Morty are playing Minecraft, they have to stop and go on an adventure. Morty asks, "What about Minecraft?" with Rick responding, "South Park did it 4 years ago." Morty follows by saying, "Wow! They're fast!" and Rick replies, "Yeah, or we're slow." This is a reference to the fact that episodes of South Park are made during the week before they air and episodes of Rick and Morty aren't aired until the entire season is complete.
Any time a fake commercial appears, they are single audio takes of Justin Roiland improvising as he stutters and laughs throughout them.