[Karellen]

Hi - Yes, I had those movies in a while. I do not use .nfo files.  

Ok, that will explain it. The errors are due to the mass artwork purge conducted by TheMovieDB earlier this year. Kodi is looking for the files, but they no longer exist at TheMovieDB.

What is the best way to run a batch refresh so Kodi would do all the movies with problems in a single run?

You could Refresh each movie individually, but if this affects a lot of movies it will be time consuming.

Best to set the Source from Movies to None. Let it clean library.
Then add the Source back as movies and rescrape the source.
The downside to this is you will lose any customisations you made to your library, like movie sets. Playcounts should remain if you don't shuffle your files around.