Well, I think, ‘fine tuning’ is the only thing native speakers of German or other Germanic languages need in English.
I can get along well enough by applying German grammar to English. However, it won’t be completely natural.
As for native speakers of a not related mother tongue - say an Asian language, for example - English has many of the same difficulties that all European languages have. For example articles as such. Of course, in English you don’t have to distinguish genders that much, but you still have to think about where to put an article at all and where not (as in ‘I eat cake’ as opposed to ‘I eat the cake’). Another thing is that English has (due to it’s reduced declination system) a quite fixed word order and this might also be difficult (for me as well, who is tending to apply German word order often enough). And, above all, tense. There are so many languages that get along with about three tenses. English has a lot and also quite strict rules as to when to use them. For example, both in French and in German, the past tenses are rarely mixed. We have a narrative past tense and one that is focused on the present, i.e. it is expressing that the thing I tell at the moment happened in the past. However, either you are telling a story (writing a book or whatsoever) or you just refer to the past as opposed to present in a conversation, so most of the time, you just stick to one tense throughout your speech. In English, you use tenses much more freely and you additionally have all these progressive forms, so it can really be quite difficult.
Then you have those tiny differences ‘will go’ or ‘going to go’…
Japanese has a progressive form, but on the other hand it’s only got past and present forms (no future or past perfect or similar), so you have just 4 tenses (progressive and not progressive, in present as well as in past tense), so for Japanese speakers as well, English offers a huge variety of tenses.
I can also imagine that for people who come from a not European background (i.e. their mothertongue is not European), it is also quite difficult to get a grip on the remainders of declinations and conjugations in English, BECAUSE there is no complete pattern anymore, but only remainders like ‘who - whose - whom’, ‘he - his - him’, ‘am - are - is - are’. Maybe it’s easier to understand the concept of different cases when learning a language that still uses the complete pattern. Although this is probably harder in the beginning, one day you will just have gotten used to it, whereas in English you can get along fairly well without having a clue what all this is about and get the same problems later on.
However, about what you said about wrong pronounciations: this is true in any language. Everyone will try to understand foreigners and understand people with a heavy foreign accent and grammar mistakes, as long as it doesn’t change the meaning of the sentence. (Germans have no problem at all understanding people who get genders wrong or use wrong plural forms or similar) However, when learning a language, everyone is aiming for proficiency, I think… and if you’re aiming for proficiency, you’re aiming for a good pronounciation, too.
Thank you!