I don't think there is anything wrong with STORING things in these containers, just heating them up. I believe that Saran Wrap releases some chemicals when heated, and if it touches any food while being heated, that food could get contaminated. I think this goes for many plastics, but only during the heating process.
Saran plastic wrap is made with a PCB plasticizer, which is an endocrine disruptor. It's generally a better idea to buy a plastic wrap made from polyethylene, such as Glad brand wrap. There are also plenty of generic plastic wraps made from polyethylene. This is mainly an environmental issue more than a food safety issue; there's a lot of waste PCBs that end up getting dumped into the environment when Saran wrap is manufactured, while the manufacturing process for polyethylene is relatively benign.
As for personal health risks, the only time you really need to worry is if you heat food while it's in contact with the plastic wrap. Sometimes this happens when people microwave food without taking the plastic cover off. Even then, the danger is pretty negligible. Simply storing food under Saran wrap isn't anything to be concerned about.
It's kind of sad that people freak out about plastics for no good reason. Some people seem to have a mentality that anything 'artificial' is bad, while anything 'natural' is good, despite whatever the evidence says.
Well . . . we all have own definitions of "good reason" as well as our own standard of "evidence". To each there own. Personally, I find most difference interesting rather than sad.
Well, it's sad when people spend a lot of time worrying about the wrong things. There are a lot of people who shudder at the thought of plastic touching their food, but don't worry about eating lots of food high in saturated fat. The people at the FDA are professional scientists, and very cautious and conservative. There are many, many things that the FDA has banned because there was only very slight evidence that it might be dangerous or unhealthy. There's actually been a lot of criticism of the FDA within the scientific community because the FDA tends to freak out and ban things that pose only a trivial risk to health or safety, or ban things based on inconclusive scientific evidence. Of course you can (legitimately, I think) argue that the FDA is right to be so conservative because it's better to be safe than sorry, but generally if they approve a container as being safe for food, it's safe for food.
And it's not as if there's something magically safe about glass. Boro-silicate glass can absorb and later release metals and other substances that would be unhealthy. Both plastic and glass are artificially manufactured substances. The only difference is that glass has been around a lot longer, so people don't regard it as a new or novel material.
I watched 20/20 on TV abt this topic then asked Dr. He said if it `smells' like
plastic a chemical frm vapors can go into food but in VERY small amounts.
We all have it in us now since yrs ago we knew nothing & types of plastic
were worse. Quote: short term storage in plastic containers, zipbags, butter
tubs is OK if cold. Wraps should not touch food & never used in micro's. All
micro-dinners are a 1 time use then throwout. 2nd heat releases gas that can accumulate in system. U won't die, but it will alter blood work tests if
you're a freq.-micro-meal heat & toss person. Styrofoam cups heated are a
big no. My Dr. showed me his own test of particulates in himself. He's 70 &
switched to microsafe plastic & glass & says wraps are fine on his cold sandwich. The heated chemical does stay in & doesn't pee out. The census
is that glass/enamel is best for heat. Good to cut back but I'll die of something else 1st. Thermal plastic coffee mugs are smooth sealed plastic
& still OK for those warm ups. Yes acid-foods pull some stuff in since plastic
is porous. I use glass alot because it stays hot/cold longer + see inside.