Ideally, you should be able to highlight individual words. I've had PDFs where it would only highlight the whole line. If you can't highlight a word or a line, it could be the PDF contains page images rather than pages of text. In all cases, using the Pencil tool will always work since it works in a layer above any text or images.

What is the source of the PDFs with the problem?

EDIT: Here's something else you can try. Open the PDF in Adobe Reader on your PC. If you can select text (just using the default mouse cursor), I think you should be able to do the same on the EE. However, if the default cursor instead gives you a selection box that ignores the positioning of text, then it would suggest the page is an image, not lines of text.