From what I could tell in the video, bisphenol a's a petroleum derivative that is used to harden polycarbonates. The other one, pthalates (also a petroleum derivative) is used to soften PVC. So technically, not made out of plastic, but used to make plastic.
Edit: Realized I misread your comment. Yes, the problem is with some plastic products, which use these chemicals (but not all, since the video mentioned that one hospital using safe plastic products).
I have the impression it's some plastics but not all. A rule of thumb many people up here use is to avoid plastics with recycling number 6 (polystyrene) or 7 (polycarbonate). These are said to be the worst.
Alex, does the film contain specific recommendations to consumers? (Normally I hate using the word "consumer" to mean "citizen" but in this case it could hardly be more accurate.)
Funny, my comment originally said something about Canada and I cut it out for brevity. I'll add it back. (Actually, it's not funny at all. The industry's argument appears to be: "But if we don't poison people, how will we make all those shiny plastic bottles?" With the fallback position: "How about if we just don't poison babies? Will that do?")
Bisphenol A (found mostly in hard colored plastics) is becoming particularly non grata (update: in Canada) these days.
Edit: according to the article it's also "the de facto lining used in food cans". Wow.