Interfacial shape instabilities that give rise to transient surface waves, ripples, fingers, or more complex but ordered patterns are common natural and technological phenomena, occurring during fluid flow, wetting, dewetting, adhesive failure, friction, and various biological processes. Using a Surface Forces Apparatus (SFA) and the optical interference technique employing fringes of equal chromatic order (FECO), which allows one to observe surface deformations at the nano scale during intermolecular and surface interactions, we have measured the surface deformations during polymer-polymer coalescence and film spreading on solid substrates. A new type of well-ordered transient surface wave/ripple pattern was observed during both adhesive contacts (liquid-liquid coalescence and liquid-solid spreading), which eventually disappeared, leaving smooth polymer-air or polymer-air-solid interfaces. As expected and previously observed, the more conventional type of Saffman-Taylor viscous fingering instability, and cavitation, occurred on separation. We propose an explanation for the observed phenomenon in terms of simple physical concepts, and discuss common microscopic and macroscopic, including biological and geological, situations where similar effects likely occur.