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?")
Phthalates, which are in products made of PVC plastics (like the pipes) which includes childrens toys but are also found in tons of other things like cosmetics, deodorants, and fragranced products.
Bisphenol A (BPA) is the other major offender. Many companies are at least removing from baby bottles and teethers now.