The latest update fixed these issues and the Gmail app finally has proper notifications. "Plus, notifications are now incredibly fast - up to 5x faster than in the previous version," informs Google.
Another improvement is that you can choose an alternate address when you're composing a message, just like in the desktop interface. If you've configured Gmail to allow you to send messages from other email addresses, you can just click the "from" box and pick a different address. The same feature is also available in the mobile Gmail site.
The app no longer requires you to enter your credentials periodically. "You can still choose to sign out of your account, but you won't be automatically logged out after a certain period of time has elapsed."
Unlike the Gmail app for Android, the iOS app uses a custom version of the mobile Gmail site and adds features like notifications and image upload. It makes sense to use this approach because Google can improve the app without releasing new versions, but the app is less responsive than a native application and doesn't include the standard iOS controls.
Download link: Gmail for iPhone/iPod Touch/iPad.