Which Blu-ray Player has the best/highest/most stable Blu-ray disc playback compatibility?

You might just need a firmware update from Samsung. I have an older Panasonic player model BD-10 which is one of the first blu ray in the market and have had no problem. Go online to Home Theater Magazine and read the reviews on blu ray disc player. The best entry level blu ray player in the market today are the Panasonic BD-60 and the Sony PS3 and at mid range are Panasonic BD-55, LG-390, Samsung 3600 and the OPPO. A year ago I purchased a couple of Panasonic BD-35 (which was replaced by the BD-60) for my kids for christmas and have had no problems. Hope this will help you out.