Casimir effect and van der Waals forces
You are correct in your ideas. The effect is important in the van-der-waals interaction and appears as an additional  $1/r^7$ term compared to the usual $1/r^6$ term. (This is sometimes called a retardation effect). It is present only at larger distances (a few nm) and arises only in induced-dipole interactions (dispersion interaction) because of the time it takes for the interaction to propagate between molecules. During this finite time (governed by the speed of light in the medium) the first dipole's direction has changed during the time it takes to cover distance $2r$ so that the inducing and induced dipoles become less correlated the farther the two dipoles are apart. The equation describing this effect is called the Casimir-Polder eqn. $W(r)=-23\alpha_0^3hc/(8\pi^2(4\pi\epsilon_0)^2r^7)$ where $\alpha_0 $ is the polarisability and $\epsilon_0$ the permittivity of free space.