As it turns out, error "Invalid Object Name" was caused by what an error actually say - invalid names of files and folders. All of affected entries have one or more trailing space at end of name.

In Web Client 10.3, opening a folder that have name with trailing space generate error "Invalid Object Name". In previous versions this was not an issue.

Originally, I created workflow with pattern matching to detect trailing space and dump results into database. I also search repository for entries with names with trailing space:

  *[ ]

but results of search was impossible to export: same error message "Invalid Object Name".  

Renaming was done manually, as any use of workflow, for example use activities "Find Entry" or "Rename" generated same error messages "Invalid Object Name".  

Interesting behavior I would like to mention: If renaming an entry that located in a folder with invalid name, that entry automatically moved to the parent folder of the folder with invalid name.

All of affected entries created between 2001-2005. Is it possible that version of Laserfiche at that time allow to create name of entries with trailing space?

Thank You Robert for suggestion.