We investigate the presence of secondary phases in La-doped Bi-2201 thin films grown by laser ablation. The cation ratios in the target material, the oxygen pressure, and the substrate temperature during the deposition are the main parameters determining the presence of diluted intergrowth and/or polytype aggregates. A statistical model of random intergrowth is used to analyze the x-ray diffraction (XRD) anomalies caused by hidden defects and to characterize the latter. A detailed structural XRD refinement on oriented aggregates allows us to identify the guest phase as a Bi deficient phase, Bi-1201. The occurrence of this particular embedded polytype is accompanied by a global Bi deficiency introduced in the films by the growing process and/or by the annealing treatment. The presence of La favors the Bi-1201 formation mostly as La-rich c-axis oriented aggregates. Bi excess in the target material improves considerably the crystallographic structure of Bi-2201, avoids intergrowth formation, but does not prevent the phase separation of Bi-1201 in La-doped thin films. We also investigate the influence of the deposition parameters on the type of intergrowth as well as their variation with La doping. This work introduces a specific methodology for optimizing the growth of thin films grown by laser ablation, which applies to layered oxides that admit polytypes with close formation enthalpies in their phase diagram.