"ü" is almost always represented as a single character in text encoding schemes, but I have been informed that it can also be represented as two characters. In Unicode, for example, "ü" is represented as a single "precomposed" character as 00FC. However, it exists as a less-commonly-used two-character grouping as 0075 0308.
You are encountering a strange bug or incompatibility. I suggest that it may be that the word processor program into which you are pasting the text has been set, for that document, to use a type of (old and obsolete) character encoding that does not properly recognize the "ü" character. Either that, or there is some strange problem with the way that this particular PDF you are working with has been character-encoded.
By inspecting the PDF you linked to, I see the following:
Application: LaTeX with hyperref package
PDF Producer: xdvipdfmx (0.7.9)
PDF Version: 1.5 (Acrobat 6.x)
I do not understand the implications of this, having no experience with LaTeX, but perhaps this could provide a clue.
The next step in troubleshooting the problem is to find several different PDFs from different sources and different websites that also have German in them, and see if you have the same result when you copy text out of them and paste them into whatever word processor you are using. If you cannot reproduce the problem, then it's a problem with that particular PDF.
Then you should try pasting German text with umlauts from the various different PDFs into new blank documents in different word processor programs (Apple TextEdit, Bean, Apple Pages, Microsoft Word, OpenOffice, whatever you have on hand) and see what results from that. The problem might be a quirk in one particular word processing program and its preference settings.
I assure you that it is highly unlikely that you are having any kind of problem with the Mac OS X operating system itself. I routinely work with writing text and making PDFs in several languages with diacriticals, including German, Spanish, Italian, and French, and I have never encountered a problem like that which you are reporting.