I did a little bit of research on these for my degree so I hope this helps! The idea for open rotor power plants (propfans) was developed because of the obvious benefit of high bypas ratio engines. High bypass ratios (BPR) mean that the mean jet velocity is reduced and the propulsive efficiency is increased. The Specific Fuel Consumption is also improved in engines with high BPR. But with conventional engines, the BPR is limited by size of the engine nacelle. Typically values of 8-10 are difficult to exceed as the increased weight and drag of the large engine makes the improved SFC useless. Hence the birth of propfans which can have one or two stages of fan not enclosed in the nacelle.
The problems are similar to those of turboprops at the higher mach numbers. The blade tips go supersonic and causes increased noise/vibration and loss of efficiency. However, designers developed sophisticated blades which are very thin, highly cambered and have substantial sweepback near the tips which delays the onset of shockwaves. This meant that efficiency and acceptable noise levels could be maintained up to Mach 0.8. Other problems were caused by gearbox design due the large amounts of power involved. Particularly with the rear mounted unducted fan (UDF) case on the MD80 where they were at the rear of the engine in the hot jet efflux.
Back in the 80's when these things were under trial, the values of sfc were approx 25% lower than those of turbofans and BPR was in the region of 30-40. So they did look pretty desirable but like the turbo-prop it has unavoidable limitations which seem to condemn it to the drawing board.