I wish to "predict" the number of bugs my company will cause using a linear regression. For any given piece of development, the prediction is not great ($r^2 = .2$). However, my real task is to predict, company-wide, how many bugs we'll produce in a week. My errors are roughly zero-mean, so in this aggregated data set my $r^2$ is closer to .8.

How should I report this? My coworkers (and admittedly myself) are not terribly familiar with statistics, but if I say something like "20% of the variance is 'explained' by the model" that makes it sound as if there is a long way to go. If 80% is explained, that seems quite good.

Am I unfairly increasing my perceived correctness if I report the higher $r^2$ from the aggregate model?

As long as you make it clear what you are predicting (bugs in a given week rather than bugs in a given project), you should use the $R^2$ from the aggregate model.
It would be dishonest to present the model predicting the number of bugs in a given project but give the $R^2$ from the aggregate model, of course.