We present our initial experiments on binary classification of sentences into linguistically correct versus incorrect ones in Swedish using the DaLAJ dataset (Volodina et al., 2021a). The nature of the task is bordering on linguistic acceptability judgments, on the one hand, and on grammatical error detection task, on the other. The experiments include models trained with different input features and on different variations of the training, validation, and test splits. We also analyze the results focusing on different error types and errors made on different proficiency levels. Apart from insights into which features and approaches work well for this task, we present first benchmark results on this dataset. The implementation is based on a bidirectional LSTM network and pretrained FastText embeddings, BERT embeddings, own word and character embeddings, as well as part-of-speech tags and dependency labels as input features. The best model used BERT embeddings and a training and validation set enriched with additional correct sentences. It reached an accuracy of 73% on one of three test sets used in the evaluation. These promising results illustrate that the data and format of DaLAJ make a valuable new resource for research in acceptability judgements in Swedish.