You make a good point that simply making charts digital is not enough. A good system detects errors, supports reporting after-the fact, and allows for good auditing. Our healthcare system has had an EMR for nearly a decade, and I've had a chance to see the growing pains and thrills over that time. Here are a few benefits that come to mind.
Auditing. I help an audit team look at who's pulling up whose records. With paper, this would be nearly impossible, but with electronic records it's quite easy to see that user X is pulling up the medical records of their ex-wife or the visiting famous person. Though this has been hard for some, I think it's made our organization much more respectful of a patient's privacy.
Moves. We moved our hospital recently and I got to write the system that tracked each patient as they went through the various staging areas to their new bed across town. Our EMR made this like tracking packages in FedEx and it worked great.
Widespread Communication. On a more practical note, this is the big one. It used to be very difficult to move charts and images around town or even to other cities. Now people anywhere in the sprawling healthcare system can see the latest on your medical condition.
Reporting. We have a massive data warehouse that lets us see the effect of our various health improvement efforts and gives us the ability to more accurately report quality data (e.g. are we giving asprin to everyone who comes in with chest pain?). Evidence based medicine is big in our organization, and it requires good data to support it.
Fixing Errors Before They Happen.
This is the most challenging one, and I think we're still in our infancy. I helped make a lab cross-reference system whose purpose is to make sure nurses know what lab a doctor really ordered. If they ordered something vaguely cryptic, they can key in the lab name and it will give them the different names in different electronic systems, in addition to hand-entered names that some doctors use.
EMRs alone aren't going to improve healthcare greatly, but they open up a lot of other options that most certainly will.