The Internet is the world's largest library. It's just that all the books are on the floor.
-- John Allen Paulos
Reading this just before I published it, I realized I should define what I mean by "serious study". Serious study is opposed to shallow reading, which is very good for exploratory learning, and the web is more helpful with, though still not sufficient. It is also opposed to directed research where you are already familiar with the area and are looking for a specific item, for which the web is very useful, though again not adequate since too much stuff still isn't on line, but it is better for this than serious study. Serious study is when you are learning a new field in depth, the equivalent of college classes. You need specific information, but even more important you need an understanding of how facts and theories relate to each other.
Scattering your attention; the Web simply has too many distractions. It's hard to study from the web for the same reason most real studying in libraries is done in carrels rather than at tables.
Very hard and time consuming to find useful information; Google is NOT adequate. Google's ranking by links is a measure of popularity not value. It could be improved for this purpose, but made harder to use, if you could restrict "links from" in some way. I've had somewhat more luck in browsing blogs related to the topic, then following links from there - but that's still time consuming following the blogs. Bruce Schneier's blog, Freedom to Tinker, and Overcoming Bias have been the most productive recently for me.
Most pages are very shallow; many others are too narrow for learning, though decent papers for those already knowledgeable in field for research. Too much emphasis on new results, but most new results are wrong, many of the rest are incomplete. There are reprints of some older papers with proven value, but they are often hard to find.
Another problem that I have, from what I've read it doesn't seem to be a common problem though, is that I read easily and quickly from the screen, but have retention and recall difficulties for what I read on screen. This is one reason I tend to concentrate on blogs, very short pieces tend to be more memorable.