The is this new modern Shopping Center with some shops, mostly empty of customers, I guess this place is new and looking forward for the future with the development of this town. There is also supermarket in a hidden place here where you can buy some supply if you need any.
Down in the center of town, just next to the bus station there is the Spar shop which is excellent for own groceries shopping and supply if you need any. They have all kind of stuff as you can expect including some beer even from your own country. (depends where are you from :)
On every Friday there is the street market of Playa de Mogán, to be honest, crowded and not any special, no the items and not the prices. Most important, watch out your own wallet not to be snatched.