We have CPOE (comp. physician order entry) and I love it. Not only can the physician enter orders, but if need be we can place verbal orders on the computer much the same as the old way of writing them out as vo's.
We have just now gone completely paperless on discharge orders, too. The physician must select all previously reconciled home meds/meds ordered inpatient, place all future f/u appts in the orders, and add all activity/diet/work/etc orders by simply checking boxes. It's soooo simple, we as RN's must make sure that ALL home meds are in the computer or else all will fail. If the home meds are not reconciled, the person cannot be discharged, period. I'm sure there will be some crusty insistent MD's who will balk at these changes, but overall, it is so much better than trying to make out that handwriting that previously couldn't be trusted without clarification on a med, that went on to write illegible discharge instructions.
I'm not sure of what system our hospital is on, I'd guess it's meditech or something similar. Even all the rehab/PT/OT/Speech notes and things are computerized now.
It was a tough transition originally for me to go from paper to this, but now when I get pulled to a paper floor, it about kills me.
Oh, and to answer the OP problem of missed orders, all "new" and orders that have not been "noted" by an RN are in blue. Once noted, they turn black. If it's something written on your shift but not due til the next, we leave it blue so the next RN sees it and has to note and implement the order, ie.. labs that are due at 0500 the next morning, or a head CT c and s contrast at 0500, that sort of thing.
Orders will still get missed from time to time, it's bound to happen. Much much less than when we were paper though, I'm sure of it.
We do 12 hour chart checks in our assessments on the computer. We simply do them under "shift summary" in the focus note section. Very simple.