When human beings enter a new country, they tend to compare everything they see with what they had previously experienced. They tend to think that what they experienced until then was "right" and that what they see is somewhat "wrong". In a Korean context, Koreans bumping into you and not excusing themselves is "wrong" because the "right" thing to do in your country is to excuse yourself.
The same thing happens when people learn a new language. Foreigners learning Korean tend to think that a lot of the aspects of Korean language are "wrong" and that the way to say things in our language is "right". It is something hidden in the subconscious, but when people learn foreign languages, they tend to use the same grammatical structures, pronunciation, word formation rules and meanings of words as in their native language.
Linguists argue that Korean is a "mirror" language of English. That is, if you put English on a mirror, you will get the Korean word order. Verbs at the end, post-positions instead of prepositions etc.
However, when Koreans speak English, they have their rules, which they think of as best, and when Americans speak Korean they have their rules which they think of as best.
Korean has different pronunciation rules from English which are as follows:
-There can not be two consonants at the beginning of a word or syllable
Therefore Koreans will add the "eu" (으) sound between consonants at the beginning of a syllable: Christmas becomes "Keurismaseu"
-Some sounds have to be followed by vowels in Korean: ㅎ (h), ㅅ (s), ㅈ (j), ㅊ(ch), ㅌ (t), ㅋ (k) have to be followed by vowels. Therefore, if such sounds are placed at the end of a syllable in English, Koreans will add "eu"(으), and "i"(이) if they are "j" or "ch" sounds at the end of a word: "mask" becomes "maseukeu", "bench" becomes "benchi"
-Some English sounds (mostly consonants)do not exist in Korean. They will therefore either be replaced by Korean consonants or will alter between them.
"f" will tend to become "p", "z" will become "j", "r" will either become "l" or a "flapped r", "th" will become "d" or "s", "v" will become "b". Note however that Koreans alter such consonants and give them "allophonic" values, meaning that they are the same sound but change pronunciation depending whether they are preceded by a consonant, vowel or nothing. "p", "b", "f" and "v" tend to have the same value among Korean speakers as they may say things like "vanana" instead of "banana", "fancake" instead of "pancake" etc. They may also say "Zames" instead of "James" and the like.
Korean is an agglutinative language where parts which have meaning stick together to form words in a regular way. If one combination is word parts is possible in Korean, it is possible for all other words. Explaining this would involve complicated "morphological" analysis so let's just put it this way:
In Korean, 조심-스럽-게, 건강-스럽-게 or 흥미-럽-게 are all possible words (note that 스럽다 becomes 럽다 when preceded by a consonant), as is any adjective with 스럽/럽 and 게. If Koreans know that "care-FUL-LY" is a possible word, they will think it is possible with all adjectives: "health-FUL-LY", "interest-FUL-LY" etc.
There are a number of grammar rules that Koreans calque from their native language when they speak English. An example of this would be that Koreans do not need an auxiliary (to be) when an adjective becomes a verb: to be handsome in Korean would be literally "to handsome". In fact Koreans tend to drop the verb "be" all together. Therefore "he's gonna come" becomes "he gonna come" etc.
Koreans also use particles differently, since they are used differently in Korean. For, to, at, from etc. are all used differently from American English. Koreans may say "I gave it for someone" instead of "to someone" etc. because in this case 에게 can sometimes be used in contexts meaning "for" in Korean (ㅇㅇ에게 케익 만들었다= I made cake for someone).
Koreans may add articles to names of people, cities and countries (the Australia, the New York, the James) because in Korean, if you apply a preposition to a noun, it should be applied to all nouns in the context
While Koreans use "the" a lot, the preposition "a" seems to be omitted. Koreans will often say "I am man" or in some cases "I man" (instead of I am a man) or "He works for company" (instead of "he works for a company". That is because in Korean there is no equivalent of the preposition "a".
SEMANTICS AND MEANING
Korean has a lot of loanwords from English which experienced semantic change over the years. Some words were also loaned from British English, from 19th Century American English through Japan or recently from Singapore, and have different meanings in American English today.
Koreans still borrow words from English and use them differently, not because they are stupid, but because they have a different vision of words and life.
Koreans may use "one piece", "hand phone", "overeat" in English sentences to mean "dress", "cell phone" or "throw up". A large number of technical terms were coined in Korean with no equivalent in American English. Americans working in the broadcasting industry in Korea may hear a lot of words they are not familiar with, including "VJ" (video journalist), "announcer" (reporter), "UCC" (video as in youtube video), "NG" (no good, when the scene needs to be shot over again) etc. Koreans use such words when they speak English.
As I argued, they "calque" Korean when they speak English, which is something every human being does when he speaks a second language. Calling Koreans "stupid" for not being able to learn and use English "properly" is equivalent to calling human beings "stupid" for having unsophisticated brains which calque native languages when they speak foreign languages.