I have had a few discs in the past give a couple of my different DVD players trouble similar to what you are experiencing, including the illusive "Dirty Disc" message, even when the disc appears to be clean. If you have just recently purchased Black Hawk Down, I absolutely recommend that you take it back immediately for a replacement and attempt to play the new disc on both of your DVD players. The substrate that the DVD information resides on sometimes can be microscopically torn or otherwise corrupted during production. If this problem continues to occur, even after replacing the disc, you may want to check with the customer service of your DVD player and see if this is a known problem that exists in that product line. From what you have said, this sounds like it is the disc causing the problem though. The Matrix DVD caused some early DVD players to freeze up, randomly skip chapters and on some, would just plain not work at all, so it is not an uncommon occurrence.
I forgot which DVD player you said that you owned, was it the Sony DVP-9000ES?
I personally have owned a Sony DVP-S3000, a Panasonic A-120, Sony DVP-NS700P(my current reference model/Progressive Scan), a Pioneer DV-343, and a Sony DAV-S300 Dream Theater mini DVD system (my wife?s, in our bedroom

. The player that gave me the most trouble was my Pansonic player (same make that GONK had problems with), but I think that was because it was a second generation unit, as well as one of their lowest end models.
I hope that a new copy of that DVD will solve your problem.
P.S. I see that you are looking for a new progressive scan DVD player. If I might inquire, what is you current budget for a replacement for you current Prog. Scan model? Have you already decided which player to get?
Once Again, good luck Lena!
-Jeremy