The first big issue is legibility. While you can use digital techniques to reveal hidden text, look into the spines of bound volumes, and do all sorts of fancy things to improve legibility, these are specialised applications that are costly and require one-off handling. Deliverability of images is one of the main issues that leads to compromise, especially with large format material with fine detail. It's hard to capture fine detail without building large digital files, and these take a long time to send down the wire, and a long time to print. Thankfully, our approaches to compressing and delivering such material are getting better all the time, but it's still common for users to be frustrated by delays in access, and by the necessity of moving around the page to read the text.
Digital images are often just that - images.
To make the information they contain more accessible we often want to also create searchable text. Again, it is improving all the time, but we shouldn't assume we can automatically convert handwritten, or even printed text with a variety of type faces in poor condition, into highly accurate searchable text. One pitfall is to ignore the very large investment sometimes required in organising and describing material, and in designing user interfaces that work. Finally, there are a host of issues to do with ownership, rights of access, and cultural sensitivities that really have to be addressed. So, there are some issues that can interfere with access, even though access is what digitisation does most excellently.