Years later I'm picking up TF2 again, and this time I'm looking into the modding community, too. With all the customization HUDs, I think I got the answer now:

**TF2 does not render the `Verdana` font correctly, somehow, on Windows. Changing `Verdana` to some other font, say, `TF2 Secondary`, will fix it.**

I used the `GCFScape` software to unpack `Team Fortress 2\tf\tf2_misc_dir.vpk`, and extracted the folders `resource` and `scripts` under `Team Fortress 2\tf\custom\hud`. Then I opened `Team Fortress 2\tf\custom\hud\resource\clientscheme.res` with a text editor, and searched and replaced 'Verdana' with 'TF2 Secondary', issues gone.

Although in the original configuration, 

    "Default"
    {
    	"1"
    	{
    	"name"		"Verdana"
    	"tall"		"12"
    	"weight"	"900"
    	"range"		"0x0000 0x017F" //	Basic Latin, Latin-1 Supplement, Latin Extended-A
    	"yres"	"480 599"
    	}
    ...

the range 0x017F should be able to cover the letter Ü (0x00DC). But it just doesn't work with Verdana and the current TF2 build 9089314.