When I start the game There is a message:
'Galaxy Updater encountered an error and could not continue: ''Updater failed moving files'' '
Then I am able to log in, but when I enter in the game it tells me that the authentication failed
Why????

I'm also encountered the same error on launcher startup and seems the login problem is exactly the same

Try this solution posted by staff in a topic that strangely has the exact same name as this one :P

"Please send your logs to us. Instruction can be found here: http://www.gog.com/forum/witcher_adventure_game_the_online_beta/game_launcher_feedback_post_here/post1.
For now try removing these files (if exist) and restart the Launcher:
1. /tmp/galaxyservice.txt
2. /Users/Shared/Galaxy/Tokens.json
3. In worst cases feel free to remove whole "/Users/Shared/Galaxy" folder."

Ah, seems i have found the solution. It is a launcher update issue. I have fixed it by copying and overwriting when prompted all files from \ProgramData\GalaxyClient\downloads\GalaxyClient into \Program Files (x86)\GalaxyClient

Thanks for providing that. Hopefully it will help my friend who is having the same issue.

I wonder how many of these issues are caused by Windows User Account Control(UAC) function and installing stuff in a protected directory? I.e. \Program Files(x86) The moment I started using Windows 7, I stopped installing anything there as it caused countless issues.

Was having the same issue detailed in OP's post, however your solution solved this. Thanks!

I agree, I hate forced installs. My C drive is meant for system/OS files and programs only. I'll try this solution here and see what happens.


UPDATE:
still the same issue for me. I'll upload my logs and see if they can figure it out.