A quick start:
* The separation of different forms of content: They don't really mix text with video, images and graphics, even though most web-native bloggers will do it. They seem to lack fluency with mixing media; it's a project for them. They'll staple a video and decorate text with images and graphics, but they don't really commuicate with it; they don't say, 'here's how Clinton responded to Sanders:" , or, 'here was the scene when the earthquake struck' , or even in a movie review, here's what the scene looks like: or . Instead, they try to describe the visual with text. Even explanatory graphics are a separate, special production, on a separate page.
* The font in their title: Back when printing fancy fonts was a technological feat, this font communicated that they were serious and sophisticated. Now, if you step back and ignore the history, it looks like a kid playing with fonts. (Look at it this way: would you ever use that font on a website you were designing?). It says, insists even: We're anchored to the paper age and will never let go. We're the old, dying generation. If you want something new, go elsewhere.
* The discoverability of content: Obviously mimicing a newspaper, but a bad choice for the web. How many links are on that home page (scroll down)? And even more content doesn't even appear there. All that hard work and content, unlikely ever to be found, buried and lost forever. It's tragic. But that's what they did in the hard copy newspaper so I guess it's ok.
* Also, where are stories updated since I visited a couple hours ago? Oh look, if I look at every link a red 'updated' indicator is next to some links (just like the web 20 years ago!), which I see if I examine every one of them (and how do I identify brand new links in this massive page of links?) - but where in this multi-page story are the new parts? I guess I'll just re-read the whole thing.
I say this all out of love. They are an very important institution. The news business is hard enough; stop handicapping yourselves! From the outside they look like they still, in 2015, haven't fully embraced the new technology. What would you say about another business' web team (that was not adapting a newspaper to the web) that produced a site that looked like this? Egads. [1]
EDIT: Some minor edits and additions
[1] I'm not blaming the web developers; I assume they are working within the general constraint of: Make it look like the newspaper.