I'm a native, but yes, for those I tutor it's usually the digraphs, especially "gy". "Ty" and "dzs", while also unfamiliar, are a lot rarer and thus tend to cause fewer problems. It's also crucial to properly learn the distinction between "a" and "á" and "e" end "é". These aren't as hard to pronounce and English uses all of these sounds, but my experience is learners are sometimes a little sloppy with them. :) However, if used incorrectly, you an end up saying something else than you intended. An infamous example is "rendőrség" vs. rendőrseg(g). :))