As Brich said, they can clog filters, not to mention when it does start to take over the top of your tank, it can block a lot of light getting to the bottom IF you have other plants in there...It might sound crazy, but I've always wanted to give duckweed a try. I like the nutrient values as well as it makes the lighing appear in an aquarium. I mean whjat even are the disadvantages of duckweed besides it growing out of control? Haha
and if Biggles was still here, he'd tell you stories of how he once forgot to wash his arm off properly, and had duckweed stuck to his arm all day without noticing it...