The omission of relevant variables can cause ßs to be biased, E[ßhat] is not equal to ß; this is a more serious cost than the loss of degrees of freedom from including irrelevant variables.

The cost of including irrelevant variables is a loss of degrees of freedom.

With every additional explanatory variable, R^2 increases (one should be aware of this so as to not take the increase of R^2 to mean something very good).