Alzheimer’s disease (AD) represents a major problem for society and a heavy burden for those affected. The study of changes in speech offers a potential means for large-scale AD screening that is non-invasive and inexpensive. Automatic Speech Recognition (ASR) is necessary for a fully automated system. We compare different ASR systems in terms of Word Error Rate (WER) using a publicly available benchmark dataset of speech recordings of AD patients and controls. Furthermore, this study is the first to quantify how popular linguistic features change when replacing manual transcriptions with ASR output. This contributes to the understanding of linguistic features in the context of AD detection. Moreover, we investigate how ASR affects AD classification performance by implementing two popular approaches: A fine-tuned BERT model, and Random Forest on popular linguistic features. Our results show best classification performance when using manual transcripts, but the degradation when using ASR is not dramatic. Performance stays strong, achieving an AUROC of 0.87. Our BERT-based approach is affected more strongly by ASR transcription errors than the simpler and more explainable approach based on linguistic features.