The phrase "sides of the mixing bowl" refers to the inner walls of a bowl used for mixing ingredients. In a figurative sense, it means considering all aspects of a situation or topic and not leaving anything out. Full definition
Start of 4 hr rise — I added the missing cup of flour, used stand mixer to incorporated until dough released from sides of mixing bowl. (chezpim.com)
Scrape down sides of mixing bowl with rubber spatula, and pour mixture over crust. (vegetariantimes.com)
Scrape down sides of mixing bowl (you may need to do this a couple of times) and beat cake batter on medium / high speed for about 1 minute so that the batter is fluffy. (mummymade.it)