We also had to wait I believe it was for a fax from Panama City HQ about our entry papers giving clearance to enter Panama. It took about an hour. But ! The police/ military office where we sat waiting has high speed open wifi. So waiting wasn't so bad.
When we arrived at the border, we got stamped out of CR in 2 minutes, but had to wait to buy insurance. The office was closed , so we went for lunch at the border restaurant .Soon there was 4-5 people milling around the ins office as we ate. Soon enough, someone showed up and we got the ins. The ride on the Panama side is great.