According to http://webaim.org/standards/wcag/checklist#sc2.4.4
2.4.4 Link Purpose (In Context) (Level A)
The purpose of each link (or form image button or image map hotspot) can be determined from the link text alone, or from the link text and its context (e.g., surrounding paragraph, list item, table cell, or table headers). Links (or form image buttons) with the same text that go to different locations are readily distinguishable.
and so WAVE (Web Accessibility Evaluation Tool - http://wave.webaim.org) says all my "details" links are not recommended on my page here:
but I can't think what would work better. I don't really want to clutter up the page with the first few characters of the actual details text because I think it would make the page look too cluttered.
Well, there are many ways you could solve your problem. To name a few:
Please also see: http://www.w3.org/WAI/WCAG20/quickref/#qr-navigation-mechanisms-refs for other options.