For my wife the hardest thing is English pronunciation of vowels; there are 37 different vowel sounds for 5 vowels (excluding the y and h). She is from Chile; Spanish, and I believe Romanian, Italian, Portuguese, French, have 5 sounds for 5 vowels. It's a tough transition, one that costs native speakers as well.
People are also challenged by the volume of words in English and the little understood English subjunctive tenses.
If there must be trouble, let it be in my day, that my child may have peace. Thomas Paine