If you click on an addon that shows a new version you will be able to show the changelog by clicking hte blue "chnagelog" text. This open the changelog in a popup.
Click on the "Update" button:
-The update will be downloaded
-In the background you can see the download&install progress bar for that addon too
-The addon will move from the top of the addon list to its place in the alphabetical order
-The change log popup will be shown in the front all the time
-The "Update" button of the changelog popup changed its text to "Installed" and was greyed out
If you close the change log popup window then you'll get back to the addon description popup:
-The button "Update" is still shown?
-You are able to click the button, and the download will repeat + installation will repeat too (as it seems)
-The addon in the list will show the update progesss bar again, but this time it gets stuck in between or at the end
-Inside the addon folder (c:\users\<username>\documents\Elder Scrolls Online\live<eu>\Addons) there is sometimes the ZIP arhcive of the addon and it won#t be extracted properly. Sometimes it is deleted correctly after the addon was installed before from the changelog.