Emile:
I think the biggest problem for foreign learners isn't irregulars, but the preposition in phrasal verbs - the way say "give up", "give in", "give out" or "get up", "get away", "get about" etc. all mean different things that can't just be deduced by what you know about the verb or the preposition alone.
These are indeed very difficult, but in my experience (and also from my observations of other fluent non-native English speakers), by far the hardest problem is the definite article. With a lot of practice and experience, you learn to use it with perhaps 90% or 95% accuracy, but then your improvement stagnates and it's impossible to ever get it 100% right like a native speaker.
Possible; most non-native spakers I know in "real life" are French, Chinese or German, and articles in French and German are close enough to English. If, as your name suggests, you know more people speaking Slavic languages, you might get a different impression. From Wikipedia (featuring a nice map!):
...Linguists believe the common ancestor of the Indo-European languages, Proto Indo-European, did not have articles. Most of the languages in this family do not have definite or indefinite articles; there is no article in Latin, Sanskrit, Persian, nor
In Russian we have the word 'Mirozdanie', which means all that exists, no matter do we know anything about it or not. The sense of this word includes you and me and every man, and every star, and every planet and all universes and all space (super) civilizations, if exist, and this world and any other worlds, if exist, and so on. Is any English word with the same sense? Or in other words, how correctly and adequately translate the Russian word 'Mirozdanie' in English? I have my web project (in Russian) “Dossier on Mirozdanie” ( http://www.mirozdanie.narod.ru ) To tell about it in English sometimes I use the word, that Google and other dictionaries recomend - 'Creation' (Creation Dossier), sometimes, when I am afraid of being accused of creationism, I use the word «Multiverse» (Multiverse Dossier), but I think, every of this words has a great shortage in the context - both of them are based on hypothetical conceptions.