Dividends are sometimes said to have been paid "out of retained earnings". What is the error, if any, in that statement?

What I understood is that dividends can be paid out in the form of a cheque (cash), in form of additional stock chasere of the issuing corporation, and in form of assets from the issuing corporation or another corporation. But I did not find anything that said I can dividends can be paid out of retained earnings.

This will give you a pretty good idea of the relationship between dividends and retained earnings:
http://www.investopedia.com/articles/fundamental/03/102903.asp

Please watch the dates on the threads. If you're using the search function, it tends to pull up old junk.