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.

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.