How does a small range of the dependent variable affects linear regression? In my regression model, the dependent variable has just a range of 96-100 with a mean of 99.73. My questions are:
1.) (How) Does this affect the quality of the linear regression model?
2.) What would be a reasonable way to take this into account?
Thanks in advance!

Since your DV is naturally bounded between 0 and 100, but you have only observed values larger than 96, the lower bound is probably not going to be a problem. (Otherwise I would have looked at a beta regression or similar.)
With a large number of observations at or near 100, it sounds like you might have inflation at this point. One simple way of dealing with this is to flip your DV (so you have values between 0 and 4, many zeros, and a mean of 0.27), and then use a zero-inflated model. Since you have continuous data, this should not be something like a ZIP (zero inflated Poisson), but a zero inflated gamma regression would be worth looking at. This will give you sensible predictions (not below zero; unbounded above, though - but you could also look at zero inflated beta regression, I just think that is somewhat less common).
As to how the boundedness and (apparent) inflation affects the quality of your or any other model, that is hard to answer. After all, compared to what? You can't really compare the performance of your model to its performance on unbounded, un-inflated data, and think that any difference is very meaningful...
