No, you don't have to do anything, except running the script to download and install the new version.
I put the script that is used to update in a file, so I just have to click the file to start a update.
Code:
#!/bin/bash
sudo -S python -c "import sys; py3 = sys.version_info[0] > 2; u = __import__('urllib.request' if py3 else 'urllib', fromlist=1); exec(u.urlopen('http://status.calibre-ebook.com/linux_installer').read()); main(install_dir='/opt')"
You will automaticallly be notified about new versions when you use calibre. I have not ever had any need to update automatically. There is no problem connected to not updating and skipping a few versions. But if you experience problems, then it is a good time to update. The problems may have been fixed in a later version.
At the bottom left of calibre you can see what version you are running, and if there is a new version available.
Usually there is a new version every week on thursday or friday. But usually only minor things change, so you don't have to update every week.