As UK residents our personal experience of the Medical facilities in Mallorca is that they are excellent. We have found the hospitals to be modern, well equipped and spotlessly clean.
We have not encountered long waiting times and have been amazed at their efficiency in being able to offer immediate surgery, when in the UK this is often not the case.
The UK has a reciprocal arrangement with Europe whereby a non resident is entitled to receive the same facilities as the local native resident. However, it is important to have a EUROPEAN HEALTH INSURANCE CARD (EHIC), which is available FREE OF CHARGE from UK post offices or on-line. If you are charged for any treatment as offered by the state (private not covered) you would reclaim that cost through the EHIC card.
You may however prefer to use a private doctors surgery, of which there are very many, all of whom offer quick and efficient service and referrals as necessary. There is a cost for this.
The same situation exists for hospitals. You are covered (with the EHIC card) for any emergency or procedure in Mallorca's state hospitals, whilst again there are private hospitals offering standards that are superb.
Palma also boasts many specialist beauty/surgery clinics.