Problem: It Doesn't Work Very Well
The biggest problem with Twine right now may be that it doesn't work as well as it should. It doesn't consistently grab summary text or tags for pages you save in Twine, it doesn't recognize article authors as relevant people and it often captures summary information about the domain you're on instead of a particular page's content.
Twine founder Nova Spivack saw that I was saving pages that weren't coming in with summary information and commented on one of my items that the page at issue was irregularly formatted. That's why Twine wasn't able to analyze it, he said. That is a major problem; most of the web is made up of ugly, non-standard pages. Fundamental to the value proposition of a top-down semantic analysis tool should be the ability to discover meaning from unstructured data. Many of the other problems Twine faces will be challenging but do seem solvable. This one could be a deal breaker.
Serious researchers will also be frustrated with the lack of support for authenticated (password protected) pages and the absence of RSS feeds -though feeds may come as soon as the app is public.