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 into 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.