Plot hole: Joy and Sadness are stuck outside of the control center. They are trying to figure out how to get back, and encounter maintenance workers who are discarding old memories. The maintenance workers show that they have the power to send memories back up to the control center to be played. Why couldn't they send the core memories that Joy had back up the same way? Better yet, why not use that method to send Joy and Sadness back up to the control center? The director of the film is even aware of the plot hole, and said "Yeah, well then we wouldn't have a third act," before explaining how the idea of recalling memories was added in later, "box[ing] [the screenwriters] in a corner a little bit."
Continuity mistake: When first arriving at her new house, Riley looks around in the living room. At the end of the room, there is a spray bottle. Riley then goes upstairs. When she returns, the spray bottle is missing and no one has moved it.
Plot hole: One of the major details in the movie is that the moving truck is missing and hasn't delivered the furniture. However, after Riley's first day of school, the family can be seen eating dinner at a table in the house, before the moving truck arrived. Either that mistake somehow went unnoticed or they just expected us to believe that her family went out and bought a new table and chairs for some reason.