Tighten up admin.
I've worked in admin and I understand that we're all human and mistakes will happen, and the more admin you do the more mistakes, but...
I've been struck in my many hospital visits over the past few years just how many people approach the receptionist to be told that sorry, their appointment has been changed to another day, but they hadn't been informed. These people had sometimes taken time off work and would now have to do so again. I counted 5 of these errors in a 40 minute wait once. Something somewhere isn't right. I've currently had to phone up twice regarding appointment letters which make no sense whatsoever (duplicate appointments, procedures in the wrong order)
Make the population grateful for the NHS and be tough on extremely difficult patients.
I refer you to the thread on bringing whole families to A & E.
Clear rules about who can accompany a patient should be stated and enforced (bring in bouncers if necessary - it will be money well-spent). I get that over-worked health staff cannot take on the role of disciplining nasty customers who only understand the language of toughness/threat. Also - tighten up rules about visiting wards. Patients and staff have to endure misery due to the inconsiderate behaviour of selfish and anti-social visitors.
But the first job is an information campaign to remind people just how lucky they are to have healthcare which is free at the point of use. Get them to FEEL grateful and re-kindle a culture of respect and gratitude towards health staff and not one of entitlement.