Bittersweet nightshade berries are toxic, making this poisonous plant (Solanum dulcamara) a "noxious weed" in my book any day! Don't confuse bittersweet nightshade with Celastrus orbiculatus plants, which are better known.
Parents, you will want to identify bittersweet nightshade, scour your backyard for any plants that might be growing there, and remove them. The berries do not all ripen at the same time, meaning that a bittersweet nightshade plant can bear green, yellow, orange and red berries all at one time. This makes for a colorful display -- a display that could easily tempt young children into plucking them and eating them. I know, because I remember sampling bittersweet nightshade berries, myself as a child.
I lived, obviously.
But do you really want to take a chance? Furthermore, while, in many cases, toxic berries, leaves, etc. may cause nothing more severe than an upset stomach, you would still rather avoid that scenario if you could, right?
So make it a practice to learn how to identify poisonous plants and remove them from your yard. And just in case you are unsuccessful in doing so and your kids ingest something that they should not, be prepared to call Poison Control.