The app focuses on the videos from your subscriptions (and other videos from their activity feeds):
The subscribed channels are now displayed in a long list, but the links to YouTube's popular sections are buried at the bottom of the list. If you have many subscriptions, you'll have a hard time finding them.
YouTube now has a unified history page. That means that the desktop history page includes the videos you watch on your Android device and the history section from the Android app includes the videos you watch when you're using a computer.
While it's not a great idea to watch videos in the portrait mode, it's nice that you can read the comments or the video's description and watch the video at the same time. The previous version of the Android app didn't display a seek bar in the portrait mode, but this issue has been fixed in the latest release.
To cache the videos from your subscriptions or the videos from the "watch later" list, go to the "settings" section, tap "preloading" and enable "preload subscriptions" or "preload watch later". Note that the videos are downloaded only when the device is charging and is also using WiFi. Another downside is that you can't play videos when your device is offline. "You'll still need a connection to play the video, but once you do it's smooth sailing through the latest from your subscribed channels and Watch Later queue," informs YouTube's blog.
The YouTube app is now also a remote that lets you play videos on Google TV and other supported devices. "While the video's playing on TV, with the new YouTube app or mobile website you'll be able to use your phone to find the next great video to watch, comment, like or subscribe. We're working to make this broadly available across connected TVs and living room devices," according to YouTube.
The latest update to YouTube's app is only available for Android 4.0+ devices, but YouTube promises that it will backported to older Android versions.