We traveled in Panama for 3 weeks in August, 2010 and spent a week in Chitre at Hotel Rex. We would have stayed longer if we could have and have inquired about their monthly rates.
This hotel has been newly remodeled. It was spotless. There was nothing even remotely needing a warning as the "bathing suit poster" wrote about in her post. While we were there, a crew was working on several rooms - putting in new plumbing, flooring, etc.
This is the nicest hotel in the city center. It is located one block from the cathedral. On our floor we had the use of a large public balcony with lounge chairs that overlooked the beautiful city park. Rooms are light with large windows and immaculate. Staff was super friendly and helpful. When we arrived before check-in, we left our luggage at the desk and a bell-boy carried it upstairs and had it in the room for us when we returned. Wi-fi worked great here - we could use the Red-net government free wi-fi at the hotel since it was so closely located to the park.
We could not have had a more pleasant stay and can highly recommend this hotel.