Is there a sound in the German language that is similarly difficult for English speakers as th is for German speakers?
The ulvular trill of the German r is tricky for us. I can do it after a vowel but not very well at the start of a word.
The ch in ich takes a while to master, but mostly because beginners tend to assimilate it with English sh, not because it's terribly hard. The ch in nach is easier.
ü also takes a while to get to grips with.
I consider none of the other vowels (and diphthongs) difficult to articulate for an English speaker, but for a beginner it's natural to substitute them with a similar but different sound that's more familiar. In the same way, a English speaker with a non-rhotic accent may have a tendency to pronounce word-final -er as a schwa as in those varieties of English.
Try to speak the German word for "matchbox"
and then you know, which consonants are difficult to pronounce.
Most native English speakers have difficulties with the sound
ch, pronounced like the guttural ch in Scottish "loch."
Also, the correct pronunciation of the different forms of
r is a problem for many people from English speaking countries.
My father (American) always had huge differences with the German R. He tended to form it from the tip of the tongue (rolling). I guess the difficult part was realizing how similar the German and English versions are.
As a Brazilian, my native language is Brazilian Portuguese. I found it much, much easier to learn the German phonemes than the English ones, both to understand and to pronunce them.
However, there are some phonemes that are a bit tricky in German. The umlauted vowels are a bit of a challenge. However the
ch is way harder. I can say I did not "get it" yet.
r (uvular trill) is somewhat hard, too, but not impossible.
Try ,,tzsch''. I've seen in it only in names and even native speakers argue about how one should pronounce this. In upper saxon it is pronounced like ,,tsch'' (without the z).
It's not simply a matter of the isolated sounds; their "phonetic context" also matters. I have no problem with the sound at the end of ich, dreißig, fertig, etc. but I can't say Eichhörnchen at normal speed.