It always depends on their native language of course. Some have issues with declension of nouns and the fact that in Serbian people, animals and objects have a gender. However, a Russian friend of mine had no issues with those as both declension and gender for everything already exist in Russian.
When it comes to native Serbian speakers learning English almost everyone I ever taught had problems with pronunciation and articles. Later on continuous tenses were an issue.
When people say pronunciation is a problem in English, I always wonder which they find more difficult. Knowing the pronunciation from the spelling? Because that would seem to be problem number one, there isn't a one to one relationship between spelling and pronunciation in English. Vowels for example, can be pronounced in numerous ways, depending on the word. Or being able to actually physically produce the sounds of the language? Like I, as a native English speaker, found it difficult when I started learning Spanish to roll my Rs. I had to physically learn where to put my tongue in my mouth in order to make this sound.
@Paul Although most English sounds are easy to pronounce correctly once, by accident, knowing which one you should use each time and understanding the difference between them is difficult. For example, my, "bed" and "bad" sound just the same because in my language these are not two different sounds. When you hear a foreign language you have a tendency to assign to each sound the closest one in your language, and you both hear it and speak it that way. Anything beyond that is difficult. English has many different vowels. They all "sound the same" to me. "th" is probably physically difficult, you have to learn where to put your tongue. Aspiration is something most languages don't have and while I may be able to reproduce it on a one-time basis, speaking that way all the time would require a lot of practice and getting used to, listening and imitating. Pronunciation is difficult if it is different than in your language and English is somehow different than most other languages in this sense. I also hear some of those pronunciation differences when listening to native English speakers speaking other languages.
@Anja Apart from the obvious noun declension, verbal aspect seems to be difficult for speakers of non-Slavic languages. Pitch accent is obviously difficult to get right, but it is forgiving. So is the difference between č and ć. I also have a friend who keeps complaining about consonant groups, such as in "Trst", but still manages to pronounce them without any problem.