Merging of adjacent bubbles is a particularly important process in nucleate boiling heat transfer, bubbly two-phase flow in small tubes, and the mechanisms that dictate the Leidenfrost transition. The merging process is ultimately associated with the rupture of the liquid film separating two bubbles, and the stability of the liquid film dictates whether coalescence is likely to occur. This paper examines two methods of exploring how the molecular-level features of the thin film and its interfaces affect the stability of the film and its subsequent impact on bubble merging. One method is an extended molecular capillarity model that has been developed for a free liquid film bounded by two liquid-vapor interfacial regions. This model predicts that as film thickness diminishes, a point is reached at which the mean centerline density in the film is between the spinodal limits for the fluid, implying that the film core lacks intrinsic stability. This suggests that loss of intrinsic stability may be the mechanism for film rupture in some cases. The second method examined here is use of molecular dynamics simulations to examine film structure and stability. Simulations using a Lennard-Jones interaction potential for non-polar fluids and the SPC/E potential for water and salt water are examined. Results of these explorations indicate that for water-NaCl solution films, surface tension increases with increasing NaCl concentration. These predictions are shown to be consistent with measured surface-tension data for such solutions. The results also indicate that for pure water and NaCl solutions, below a threshold thickness, the surface tension decreases with film thickness. Wave interface stability theory implies that this tends to make the film less stable. The implications of the results of these investigations for bubble merging in two-phase flow and boiling processes are also examined.