The following problem continues:

On my master site, I select Components > Multisites > Manage Sites (Site Manager). Many slave sites have an icon next to the ID with a popup: "New extension present...". I select the slave site, select Edit, make a small change, and Save.

It returns "The site '[sitename].com' is updated." but the ID icon does not go away.

Help?

The "refresh icon" is displayed when the number of table (count) is not the same between 2 websites.

Use the JMS Tool menu and select the website that correspond to the website that you want to cross-check. In the "table" tab, you will find all the tables and links of the website.
Somewhere in the list, you will have a difference. Perhaps that you have additional table in the slave site that are not present in the other website.
This might be the case when you uninstall something in the master before that you uninstall in the slave site.