Signal values we will 'miss' between sampling instances during sampling of band limited signals
I don't have a real answer but I have the feeling that this result will help you out: Bernstein's inequality says that, if the signal $x(t)$ is bandlimited to $|f|\leq B$, then $$\left| \frac{\textrm{d}x(t)}{\textrm{d}t}\right|\leq 4\pi B \,\textrm{sup}_{\tau\in\mathbb{R}}|x(\tau)| ,\,\,t\in\mathbb{R}$$ where $\textrm{sup}$ stands for "least upper bound".

I found about this inequality in Amos Lapidoth excellent (and free in PDF format) book "A Foundation in Digital Communication". A proof can be found in M. A. Pinsky, "Introduction to Fourier Analysis and Wavelets".