Noisy training data can significantly degrade the performance of language-model-based classifiers, particularly in non-topical classification tasks. In this study we designed a methodological framework to assess the impact of denoising. More specifically, we explored a range of denoising strategies for sentence-level difficulty detection, using training data derived from document-level difficulty annotations obtained through noisy crowdsourcing. Beyond monolingual settings, we also address cross-lingual transfer, where a multilingual language model is trained in one language and tested in another. We evaluate several noise reduction techniques, including Gaussian Mixture Models (GMM), Co-Teaching, Noise Transition Matrices, and Label Smoothing. Our results indicate that while BERT-based models exhibit inherent robustness to noise, incorporating explicit noise detection can further enhance performance. For our smaller dataset, GMM-based noise filtering proves particularly effective in improving prediction quality by raising the Area-Under-the-Curve score from 0.52 to 0.92, or to 0.93 when de-noising methods are combined. However, for our larger dataset, the intrinsic regularisation of pre-trained language models provides a strong baseline, with denoising methods yielding only marginal gains (from 0.92 to 0.94, while a combination of two denoising methods made no contribution). Nonetheless, removing noisy sentences (about 20\% of the dataset) helps in producing a cleaner corpus with fewer infelicities. As a result we have released the largest multilingual corpus for sentence difficulty prediction: see https://github.com/Nouran-Khallaf/denoising-difficulty