Integrated sensing and communications (ISAC) is envisioned as one of the key enablers of next-generation wireless systems, offering improved hardware, spectral, and energy efficiencies. In this paper, we consider an ISAC transceiver with an impaired uniform linear array that performs single-target detection and position estimation, and multiple-input single-output communications. A differentiable model-based learning approach is considered, which optimizes both the transmitter and the sensing receiver in an end-to-end manner. An unsupervised loss function that enables impairment compensation without the need for labeled data is proposed. Semi-supervised learning strategies are also proposed, which use a combination of small amounts of labeled data and unlabeled data. Our results show that semi-supervised learning can achieve similar performance to supervised learning with 98.8% less required labeled data.