Discuss some applications of the generalized Riemann hypothesis to problems that are not at first directly about zeta or L-functions. For example, the Solovay-Strassen test leads to a polynomial-time primality test if GRH is true for all Dirichlet L-functions (well, you "just" need GRH for even characters). Of course Agrawal-Kayal-Saxena later gave an unconditional proof of that polynomial-time result, but I think the technique by which Solovay-Strassen would create a polynomial-time primality test is a nice illustration of analytic methods.
Moreover, when you do give applications of GRH, you ought to indicate what would happen in the theorem if one knew a uniform zero-free region of the form Re(s) > 1/2 + epsilon for some epsilon in (0,1/2). Many applications of GRH "only" need a common zero-free region in the critical strip, not the optimal common zero-free region Re(s) > 1/2 (at the expense of worse constants when epsilon > 0 instead of epsilon = 0).
