Melting plastic, leached chemicals and bodily burns are three risks of cooking at high temperatures in plastic bags. The FDA regulates the safety of plastic containers so that they can be used for boiling or heating foods. This also includes the cooking method called sous vide, which cooks food in water in a sealed plastic bag but below boiling temperatures.
Harvard Medical School recommends heating foods only in approved containers that are labeled as such, especially when heating in the microwave. When you sous vide, use food-grade vacuum sealing bags and only used them with a vacuum-sealing system.
Dangers of Melting
Some bags are made from plastic that is too thin to boil without melting. They recommend calling the manufacturers of the plastic bag and asking them what the softening point is.
For example, Ziploc brand bags have a softening point of 195 degrees, which means they would melt at boiling point, 212 degrees. This will ruin both the food and the dishes the bags are in.
Possibility of Chemical Leaching
When plastic is boiled, the chemicals used to produce it can leach into the food being prepared due to a high temperature. Polycarbonate plastic releases the chemical Bisphenol A (BPA), but there are other types of plastic bags, including high-density polyethylene, low-density polyethylene and polypropylene, that don't leach this chemical.
Cheap plastic bags that are sold in bulk aren't safe for cooking food in, but even with the safer bags, However, there's still a risk that these types of plastic will release non-BPA chemicals, but the specific amount and risks are unknown. To determine which type of bag is which, check that they're labeled "microwave-safe."
Risk of Burns
When water is boiled in a bag, bubbles can form, which could burst when the bag is moved. Even if the water is outside the bag, the bag itself can still burst open when temperatures get very high. If either of these two things happen, the cooks may get burns on their face or hands.
Adding salt or other spices can produce the same effect because it disturbs the bubbles that have formed, causing them to erupt. Additionally, a bag can ignite, producing a fire and subsequent burns to a person standing nearby. This is most common when using a microwave oven.