I note that the ordinals of L are the same as V, so I guess that it has no $\Pi_1^1$ consequences. On the other hand Wikipedia tells me that it asserts the existance of a $\Delta_2^1$ non-measurable set of reals. "Measurable" involves third-order concepts but I know that there's often a "coding trick" that gets around that sort of thing, so I guess it has some analytic consequences.
Of course I am guessing -- I am not very good at this stuff. But I am curious. What's the least point in the analytic hierarchy where V=L matters (if any)?