My major complaints are:

• No comments. I often disagree with articles (or find errors), and I like to leave a note. “Dead-tree” publications rarely allow you to post comments on their sites, and in the rare cases when they do they tend to be heavily moderated.
• Bad design. The web is not paper. You can’t treat a website like a newspaper/magazine. That means no “between-page” ads, and no newspaper-style front pages. Print design is not the same as web design; so if your publication is going online, hire someone who knows how to design for the web.
• Subscription content. You’re not going to get very far online if you make people pay a subscription to view your content.
• Lack of links. When “traditional” publications sites mention websites, they pretty much never link to the actual sites. Often they don’t even list the URL. Hoarding PageRank is just stupid.