A few suggestions...
1) Split TV and Radio properly, up to and including having separate public bodies running them.
Programmes like R4's Today and PM are terrible for promoting specific news stories just because Panorama or Newsnight has a "special" on that night. It would also help stop the BBC from bombarding me with Chris Bloody Evans. No other company would be allowed to own the only national DAB network, four national FM networks and the four TV channels available from every single TV mast
2) Bin all the "Me too" commercial imports and programme genres that are already well served
"The Voice" is the worst example of this. An imported Dutch format only there to compete for ratings. Eastenders is another example of a genre well served commercially.
3) Look outside the urban, metropolitan comfort zone of meeja luvvies
BBC Take note: There is a world outside London, Manchester, Cardiff and Glasgow. When there's a story of note somewhere like Wales or Cornwall, don't spend thousands on sending a crew from London so that the deputy editor for Fish can do a two minute piece to camera in the dark, use the experienced crew you have in the area. Realise that the countryside contains people and stories just as important as those in towns.
4) Stop pinching local newspaper stories for your website
It's amazing how often the BBC news site for mid Wales is updated on a Wednesday afternoon, just after the weekly local rag is sent out...
5) "The Arts" aren't really BBC territory
Why should licence fee money go to the BBC for producing arts events like the Proms? Either reduce the licence fee or use the money to set up an arts fund for independent providers.
6) End the halfway-house that is UKTV
As rubbish as Dave/Yesterday/Gold etc. are, they are 50% owned by the BBC, yet are only available to some licence payers free to air, while the rest have to pay a subscription. Either make the channels available UK-wide (either via terrestrial or FTA satellite) or force the BBC to sell its stake.