I take immaculate care of my discs. Some of them have been played exactly once. Maybe I need to return Blu-Ray player #2 and try for #3.
Were #1 & #2 the same brand / model? As NIUPonyBoy said certain brands consistently have DVD skip issues, I'd be insisting on another brand for #3.
My Oppo plays DVDs better than my Pioneer DVD player did, because it upscales them (the DVD player was fairly old).
The Oppo was an indulgence, but to my understanding most of the major brand Bluray players play DVDs perfectly. You can find online reviews for most of them.