I am using OS X Lion 10.7 with an American English keyboard. For typing German umlauts I normally just press and hold the appropriate key until the little OS X popup appears and then I can choose the umlaut.
In the TexShop editor I can do the exact same thing. I press and hold "u" for example and the little popup appears. Then I choose "2" for writing "ü" but what happens is that instead of "ü" an "u" is inserted. I also tried the Cmd+U shortcut but it shows the same weird behaviour. I don't think that it is an encoding problem because I can copy and paste umlauts in TexShop. They get displayed and I can also compile to a pdf document.
Any advice on what is wrong here?
I just found a workaround. If you press and hold the letter and then use the cursor keys to choose the umlaut it just works fine. It seems like the problem is the number keys to choose the right Umlaut from the popup.
Example for typing ü:
[Press and Hold u]- => Doesn't work!
[Press and Hold u]-[->]-[->]-[Enter] => Does work!