Pretrained models through self-supervised learning have been recently introduced for both acoustic and language modeling. Applied to spoken language understanding tasks, these models have shown their great potential by improving the state-of-the-art performances on challenging benchmark datasets. In this paper, we present an error analysis reached by the use of such models on the French MEDIA benchmark dataset, known as being one of the most challenging benchmarks for the slot filling task among all the benchmarks accessible to the entire research community. One year ago, the state-of-art system reached a Concept Error Rate (CER) of 13.6% through the use of an end-to-end neural architecture. Some months later, a cascade approach based on the sequential use of a fine-tuned wav2vec 2.0 model and a fine-tuned BERT model reaches a CER of 11.2%. This significant improvement raises questions about the type of errors that remain difficult to treat, but also about those that have been corrected using these models pre-trained through self-supervision learning on a large amount of data. This study brings some answers in order to better understand the limits of such models and open new perspectives to continue improving the performance.