Also, not a fan of the wasted space on the sides of the tweet feed. However, the new web design looks great.
In most situations, people use Timeline mentions to achieve the same thing, but without the secrecy and limitations direct messages introduce. I don't have a problem with this at all, frankly. It leaves a big opening for 3rd party clients to fill the gap, while repositioning the Twitter for iPhone app as the best choice for the mainstream Twitter user (which it wasn't previously but is as of 4.0).
It may not be in your best interests, but I think it's a smart move that's in the long term interests of the service. Twitter, from the beginning, has always been about learning from the community and observing how people use the service rather than telling them how to use the service. This is just one more lesson learned from actual users.
The rest of the UI changes are quite painful, though. I support the previously discussed changes, but overall the 4.0 update is a regression in terms of the UI.
EDIT - I write all that, then I see this in my timeline: "Twitter for iPhone pro-tip: swipe up on Me for DMs and swipe left on Me to switch accounts." I guess they found a compromise. Actually, that's pretty amazing. Nobody else has to think about DMs if they don't want to, but power users still get instant access. Great job, Twitter.
Not the most discoverable gesture, but it's there, though it's only a little weirder than "swipe across tweet for secondary actions" (though on that topic I'll miss using that to quickly save links to Instapaper).