After the stress and the hunting, my father was finally admitted to our first choice for rehab.  I have to say, it appears to be an extremely well-run facility and my sister and I are feeling a strong sense on relief that he is here and is getting the help he needs.
I'm looking back on his hospital discharge which I felt was rushed and sloppy. Medicare gives you a twenty-hour window before the hospital can place you in any facility that has a bed.  While Medicare does say that the discharge mus be "safe and adequate", there is no real definition or protocol in place to explain exactly what that should look like.
Here are some things I wish we would have done differently:

• started to look for a rehab facility the first day my father was admitted to the hospital. Instead, my sister and I both stayed with my father in the hospital when one of us should have spent that time looking at facilities.   Before his discharge we found two places that were acceptable to us and as it turned out neither had beds available.
• widened the area in which we looked.  My dad, of course, wanted to be close to his home.  However, we are fast learning that emotional comforts, such as being near his friends so they could visit, are often not feasible.
• followed up with the doctor to make sure that she did what she said she was going to do.  When the doctor found out that we were having trouble finding a place, she told us not to worry, that she could medically keep him for a couple more days.  However, she never did rescind the discharge order.  She was a resident and while she took excellent care of my father while he was in the hospital, she probably was not aware yet of all the rules required by Medicare.

We did end up appealing the discharge, which we did only to get more time.  This is what I understand about an appeal.  If you appeal the discharge you do not have to pay for the services you receive during the appeal.  Medicare will review the medical records and if they find that you do need to be discharge, they will cover your hospital services until noon of the next day.
This seems to me a very costly way to buy more time, but it finally did feel like the only option open to us.