When I have seen first time this error on Joomla 1.6 while tried to save a new article in Article Manager I was lost:

I was diggin' around to see what can be wrong, and the final clue leading me to the solution where come from a phpMyAdmin checkup. Weird thing was that the article has been saved, but I found an unexpected value in the article's database record: the article wasn't assigned to any category ID and found a value which I wasn't knowing back then what a heck is for: a column called asset_id with value set to zero.

And this clue has been leading me to the solution (BTW, first step with rebuilding the menu might be unnecessary, but I decided to leave it there - because can't harm, but might fix similar errors in menu system you are not aware of - yet):

• Go to the Menu Manager – Click on Menus, Menu Manager, Click on the ‘Rebuild’ button
• You will see a message that says:
  Successfully rebuilt
• Go to the Category Manager – Click on Content, Category Manager, Click on the ‘Rebuild’ button.
• You will see a message that says:
  Categories tree data successfully rebuilt.
• Edit all your parent categories and save them.
• Edit all your sub-categories and save them.
• Go back to the Article Manager, edit all the articles that were created with the ‘Invalid Parent ID” error message and save them again.

After refreshing your menus, categories you should not have any problems creating new articles anymore. As to the existing articles that had asset_id = 0, those asset_id’s will get populated after you open and save the articles.

As you might guessed allready, the error was generated by the fact that the category tree structure was messed up for some reason. Why? Don't ask me, I 'd like to know too!