The traditional bird dog is seen as a staple in many strength and conditioning programs for its ability to help create stability through the trunk and connecting the upper and lower limbs to one another. The most common mistake that I see is an overextended lumbar spine. To combat this, try using a glider on the back foot in order to get an adequate contraction of the glutes while minimizing extension of the lower back. This will help you keep a neutral spine throughout the movement.
Another variation that can be used that also adds a little bit of rotation at both the arm and the hip can be done by placing the hand on the back of the head while driving the elbow up towards the ceiling, and bringing the knee out to the side as if you were also lifting it towards the ceiling. Although slightly more advanced because it requires a bit more mobility in the shoulder and the hip, i find it helps to avoid some of that lumbar extension i mentioned previously.
A third variation to spice it up a little bit more is the bird dog row. This adds more of a rotational component as you fight to keep your body stable as the dumbbell pulls you to one side.