The Amazing Arcade Adventure continues the graphical style of the other Math Missions games. Meaning that it shows Spectacle City (where all the action takes place) in a very cartoony style. Unfortunately, I noticed on a couple of occasions that the people of this city got choppy and distorted for no apparent reason.
There isn't really any music, per se, in this game. Mostly, you hear background noises befitting the setting of the problem (for example, you would hear construction sounds on top of the future site of the World Peace Building, or checkout counters at the Incredi-Bulk Grocery store). As far as the sound effects themselves - nothing really special. They can get a little repetitive and nerve-racking after a while, but it tends to take some time.