What’s your answer, @davidb? Great question (GQ), by the way. It might seem obvious, but I have not seen it asked here before. Welcome to fluther.
I didn’t answer the part of your question that asks about problems, but I’d say there are three with Internet research:
1. Being able to come up with the search terms that will help you zero in on your answer. Skilled researchers are very good at this, but all of us can get better with practice. The advanced options can help narrow results.
2. Being able to evaluate the quality of information and know what you can rely on. Here’s some great advice on that score. (The question buildup is long; skip to the last paragraph. Researcher ‘pinkfreud’ was Google Answers’s all-time star. She and many of her former colleagues now answer questions on Uclue, cited above.)
3. Finding information that is not available or readily findable online. Some things just aren’t and never will be. You may need (a) a book or periodical, (b) a real person, or ( c) field research.