The knot itself will not be physically weak, but a knot causes weakness in the surrounding wood because it disrupts the flow of the grain. The grain distorts around the knot and the deviation is the source of the weakness. The greater the distortion the greater the weakness. Another contributory factor is that the knot in effect causes a void in the wood. A good example would be where a knot takes up about half the width of a piece of 2 X 1 at about the midpoint of the length. If you fixed the 2 X 1 firmly edge down at one end only creating a cantilevered beam and apply downward force to the other end the chances are you'd be able to see the piece of wood deflect sharply somewhere near the knot.
If the knot is small in a large piece of wood I wouldn't worry about it from a structural point of view. The knot could fall out if it's a loose knot (aka dead knot), but will remain in place if it's an intergrown knot (aka encased or live knot). I suppose if there are voids in and around the knot bacteria could get in there, especially if the wood is unpolished in its end use form, but that would probably only be of significance if the wood is used for something like a chopping board or around some other food preparation area, and possibly if it's used for items kids are likely to chew on, eg, toys, cribs, etc. Slainte.
