The latest developments in natural language processing and machine learning have created new opportunities in legal text analysis. In particular, we look at the texts of online privacy policies after the implementation of the European General Data Protection Regulation (GDPR). We analyse 32 privacy policies to design a methodology for automated detection and assessment of compliance of these documents. Preliminary results confirm the pressing issues with current privacy policies and the beneficial use of this approach in empowering consumers in making more informed decisions. However, we also encountered several serious issues in the process. This paper introduces the challenges through concrete examples of context dependence, omission of information, and multilingualism