Dropdown Placemarks List

You don't need reinstall. All can be done by publish state.
If 2 maps is OK, and one - no, you should check objects for this map (by unpublishing all and one by one publishing). It is a problem with object (placemark), not component.
2.10.8 - fixed only admin

There is still a problem in admin panel (the same). I left only one placemark active and erase all additional html from it - it's the same...

360tv.pl/przyroda/tatry/polana-pisana

It is a new one , and it is for plugin.

I'll check it tomorrow evening.

But I ask you about admin, and you say it is the same. Very strange, check if you have latest (check by extension manager, if component v.2.10.
In JED there's not latest.

Do you install Joomla from official site, or you install a somebody's package.

Can you give me temporary access to backend, mail me ZhukDL@gmail.com