If you're self-catering, this market is your one-stop shop; if, like us, you're in a Palma Old-Town hotel, then this is where to eat really fresh food cheaply with the locals. Other posters have indicated the brilliant array of ultra-fresh meat, fish and vegetables (though I haven't read any comments on the stall with pretty much every spice in the world...it's there); for those with no possibility to take home and cook this amazing produce, it's a graze around the tapas and sushi stands that'll set you up for the day. That oyster bar is OK, but the clientele is a bit up itself; much better is the last bar in the fish market, right by the doors. They flour and fry the fish, the prawns, the squid, etc., right in front of you and slap your "racion" down with a basket of bread, a beer or a glass of dry white plonk. For about five euros a head.
King Sushi's pretty good, too; staff looked to be Thai rather than Japanese, but the fish is so fresh that only snobs/racists would care.
For authentically rib-sticking Mallorcan tapas (frito mallorquin, chickpeas, croquetas, mini-stews), the Bar Mayor is one of several around which local people congregate.
A couple of phrase-book politenesses will see you served in your turn (the market and its bars get very busy at midday), and then you can let your pointing finger do the work.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.