I actually have had some problems when running DVD movies when my PS2 was verticle. I put in one of the discs from From the Earth to the Moon and noticed that the television screen would turn black repeatedly thus making movie unwatchable. Thinking that it might be the discs\' fault, I went into the living room and put the disc in my main DVD player but it worked just fine. I\'ve since tried several other movies and they have all been doing the same thing but when I placed the PS2 horizontally I found no problems.
BTW this problem has been isolated to movies as I have yet to run into problems with any of my games.