Thats easy...it will create a ~0.7V drop in the supply voltage making the rails ~1.4V (in a bipolar design) closer to one another. In a fixed gain design this will limit the output to ~1.4V less than it could have been. The exact definition of loss in dynamics.
The thing is though: good luck noticing the loss in dynamics as it is going to be, in my opinion, negligible for most apps. As negligible as I predict that it is, I agree with the other poster who suggested a pi filter by dropping a ~100uH inductor in the place of the diode. The advantage is no junction drop, and it is linear.