The field-dependent domain structure of a ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_{3}$ thin film epitaxially grown on a ${\mathrm{LaAlO}}_{3}$ (001) substrate has been investigated at low temperatures by magnetic force microscopy. Due to the lattice mismatch, the ferromagnetic thin film is structurally disordered and exhibits a stress induced perpendicular easy axis of magnetization and stripe domains at zero field. The magnetization reversal is imaged in a movielike manner along the easy axis major hysteresis loop. Individual Barkhausen jumps are distinguished as either nucleation, growth, or annihilation processes, and analyzed with respect to size, contrast, and position. Nucleation and annihilation occur only in a limited field range just below saturation while growth due to wall propagation dominates the domain formation. The role of disorder in the material in comparison to demagnetization effects is discussed in detail, particularly with respect to the size distribution of nucleation and annihilation as well as growth processes, domain wall pinning, and preferred nucleation sites.