Mitsubishi, Kawasaki and Fuji Heavy Industries in Japan are building several of the components for the 787 and All Nippon Airways is to be the first airline to receive a 787.

http://www.seattlepi.com/business/275465_japan27.html

There were issues with where the wing meets the body (both parts built in Japan), but the responsibility supposedly lies with Boeing who designed the parts.

http://seattletimes.nwsource.com/html/boeingaerospace/200956...

Japanese and Korean suppliers are working to ramp up production of parts.

http://www.bloomberg.com/news/2010-10-01/boeing-787-supplier...