Mobile Laser Scanning (MLS) systems have proven their usefulness in the rapid and accurate acquisition of the urban environment. From the generated point clouds, street furniture can be extracted and classified without manual intervention. However, this process of acquisition and classification is not error-free, caused mainly by disturbances. This paper analyses the effect of three disturbances (point density variation, ambient noise, and occlusions) on the classification of urban objects in point clouds. From point clouds acquired in real case studies, synthetic disturbances are generated and added. The point density reduction is generated by downsampling in a voxel-wise distribution. The ambient noise is generated as random points within the bounding box of the object, and the occlusion is generated by eliminating points contained in a sphere. Samples with disturbances are classified by a pre-trained Convolutional Neural Network (CNN). The results showed different behaviours for each disturbance: density reduction affected objects depending on the object shape and dimensions, ambient noise depending on the volume of the object, while occlusions depended on their size and location. Finally, the CNN was re-trained with a percentage of synthetic samples with disturbances. An improvement in the performance of 10–40% was reported except for occlusions with a radius larger than 1 m.