I have everything working on my site but I wanted you to be aware of some issues that I came across. Hopefully I can explain it here so you can also duplication and hopefully fix.
Issue #1
Within the English domain, I edited a top level menu item (Customers) in the Primary Links and checked that this menu only shows up for English, French, German and Italian (Chinese, Simplified not checked).
Then I created a new menu item (also called Customers) to only show up for Chinese and one menu item under also only for Chinese.
Then I went to Localizer strings translation and searched on Customer. It found 2. I edited the second one and Saved.
After I did this, the new menu ended up in the English domain and no longer shows up in the Chinese domain even though the checkbox still indicates to only show of in Chinese.
What I ended up doing was not translate the Chinese menu through Localizer strings translation (admin/content/localizer/strings) but just in the menu item (admin/build/menu/item/edit).
Issues #2
I had markets, markets/industry and markets/industry/financial menu items are all pointing to the same node. This was causing a problem with my nice_menu expanding in the left column. To temporarily fix this problem I created a new node and replacing the markets/industry alias to point to this new node. Then I changed the menu for Markets->Industry to point to the markets/industry (new node) alias rather than markets/industry/financial (old node). This fixed my problem in English.
When I went to the French site to test Markets->Industry and the node/### came up rather than markets/industry. Some how this new node got created but I didn’t create it. There wasn’t previously a translated version for French and now there is. It was automatically created. Does the localizer module create this node? I have that other module that was interfering before is disabled.
Can you please see if you can duplicate either of these issues?