This paper examines two related problems from liquid-film theory. Firstly, a steady-state flow of a liquid film down a pre-wetted plate is considered, in which there is a precursor film in front of the main film. Assuming the former to be thin, a full asymptotic description of the problem is developed and simple analytical estimates for the extent and depth of the precursor film's influence on the main film are provided. Secondly, the so-called drag-out problem is considered, where an inclined plate is withdrawn from a pool of liquid. Using a combination of numerical and asymptotic means, the parameter range where the classical Landau–Levich–Wilson solution is not unique is determined.