With specific exceptions (medical devices - those Rascal ads are there for a reason) there generally isn't a ton of fraud. What there is is a lot of middlemen each taking their own cut, which cumulatively adds up to a lot of overhead. It's the "efficiency" part that you mention.
Efficiency is a tough nut to crack but there are organizations like Kaiser Permanente that have been very successful with a vertical integration model to cut this overhead. The problem is that it's a political fight every step of the way - doctors, hospitals, insurance companies, and drug makers each have their own extremely powerful lobbies who will spend lavishly to keep their cut of the profits flowing.
Which is why we're actually moving in the opposite direction - the ACA moves away from this type of integrated care organization and towards a fee-for-service model. The idea is to have the consumer be the one choosing the cheapest MRI provider or whatever - but in practice the pricing is still entirely opaque and the public are more or less thrown to the wolves. The finest health-care plan the Heritage Foundation could devise...
And of course everyone has their own idea of how to improve efficiency, all of which translates into a lot of paperwork and red tape. That is why your insurance denies claims after all - "efficiency" (airquotes). It creeps into every aspect of medical care, especially anything having to do with Federal dollars (Medicare/Medicaid). And to be fair a lot of it is justified, it is an uphill battle to get providers to adopt even basic best-practices like checklists during surgical procedures ("remove and count all 5 pieces of gauze before you close the patient"...). Another thing that doctors fight tooth and nail is clinical decision-support tools - even though these are a value-add for the physician in many cases (did you want to order that test with contrast or without? A family doctor may not know.)
(disclosure: I worked on such a tool at my current employer)
One little-addressed area of extreme waste is generic drugs. The idea is that once your patent expires (after decades of "patent evergreening" of course) anyone can make your drug - but in practice that's not how it works, one company just dumps product on the market at cost until everyone else leaves the market, at which point they are once again free to charge whatever they want. The overhead costs of starting drug production is quite high, and in practice it's more difficult for new drugs to claim bioequivalence because the drugs involve biological steps in their production. A company is not obligated to share the organisms used in their production process and if a competitor creates their own they must repeat FDA approval processes, which are inordinately expensive.