I was thinking about this some more today and one thing I'd like to get rid of is the postcode lottery. Everyone entitled to the same services across the country (ideally across the UK, but certainly across each home nation). For example, my mum lives on a county boundary and friends over the boundary find it much easier to access their GPs and also get some nursing care at home after they've had an operation. In her area there is nothing and I even needed to get shirty with her surgery to get them to send a nurse out to her to check a dressing.
Post-operative care like that should be standard, not depend on where you live or how stroppy your daughter is!
My mum also had a friend who had an accident in Germany and a nurse was sent to their caravan park every day to check their wound dressing! I can't see that happening in the UK!
Also, MIL had a fall but she was bed-bound afterwards. They wouldn't give her physio because she had dementia and wouldn't remember to do it. I feel like in other countries, someone would come round to the house every day to make sure she did it. Obviously family could as well, but physio needs to be done properly.
It's that sort of care that should be standard and might actually save money in the long run.
I think the biggest issue for the NHS is that it is too short-term-ist.
Like most things, to be fair.