Learning a language involves becoming proficient in the four skills of speaking, listening, reading and writing. Mistakes are an inevitable part of this process and neither the teacher nor the student should become fixated on them. It is useful for both, however, to have an understanding of the variety of typical errors in written English, since these are the most amenable to correction. Written errors can be categorized as errors of mechanics, grammar and usage.
Mechanical mistakes are those of orthography (spelling and capitalization) and punctuation. Everyone who writes in English makes such mistakes, whether native speaker or ESL student. In many cases mechanical errors are the consequence of quick writing where the focus is on the content rather than the form. Although English spelling is difficult, it is possible with diligent use of a dictionary and/or computer spellcheck for every writer to eradicate all or almost all of the spelling mistakes in a piece of writing.
As far as punctuation is concerned, there are a very few occasions when a non-native speaker is more prone to make a mistake than a native speaker (for example, the German student who puts a comma before the subordinate clause in reported speech.*) The most common punctuation mistakes, however, arise when the student does not correctly end a sentence (producing either a fragment or a run-on.) These are typical of immature writers who do not understand the concept of a sentence, and are neither more nor less likely to be found in an ESL student's work. More about sentence errors.
Mechanical errors seldom interfere with comprehension, but can reflect negatively on the writer, particularly in formal/academic settings. Mainstream teachers can be sure that ESL teachers will have identified students who make a large number of mechanical errors and will be working with those students to rectify the problem. Mainstream teachers are probably best advised not to make a big issue of general mechanical errors but it is not unreasonable for them to insist on the correct spelling of the key subject-specific words that are currently being learned by the whole class - photosynthesis, deforestation, hypothesis, etc. These words will no doubt have been written on the board and will appear in class and homework worksheets.
* "Reagan said, that the USSR was an evil empire."
Grammar mistakes rarely occur in native speakers' writing but very commonly do in the work of less proficient ESL students, whose mother-tongue "interferes" with the production of correct English*. ESL students make numerous mistakes in the use of verbs (for example, incorrect tense choice, incorrect tense form), the articles (a/an, the - particularly Asian students in whose languages these words do not exist), and word order.
* A typical interference mistake of a German learner of English is: "I am here since 2 weeks" instead of "I have been here for two weeks". A further example is: "I tell you tomorrow" instead of "I'll tell you tomorrow."
Grammar mistakes in writing occasionally disrupt comprehension, but usually they do not. The student who writes "I putted beaker on tripod", for example, will have conveyed his meaning perfectly intelligibly. Since there is no clear evidence that ESL students benefit from correction of grammar mistakes, even in contexts where the explicit focus of the teaching is grammar, the mainstream teacher is advised not to make a big fuss about such mistakes in pieces of science or history homework, etc. Such mistakes will disappear as the learner's interlanguage (implicit grammar system) begins to approximate the intuitive grammatical knowledge of a native speaker.
On the other hand, there is no reason why it could not be made clear to ESL students who are writing an account of a historical event, for example, that they are expected to write verbs in the past simple tense, and mistakes in this aspect of their homework will be identified.
Usage mistakes A usage mistake is a word or a string of words in a sentence that is grammatically possible*, but not usual in standard English. Hence native speakers rarely make usage mistakes, but ESL students very often do. Such mistakes frequently occur in ESL students' work when they look up a word in their own language and select the wrong English equivalent for the meaning they wish to express. Conversely, failure to use the dictionary can result in the false friends usage mistake. For example, kontollieren in German means to check (over), so the following problem in the German student's writing is not surprising: "It is important to control (i.e. check) the results carefully."
Faulty usage in larger passages of writing is often the consequence of the attempt to render word-for-word into English the mental or written version that the ESL student has in the native tongue. It is such mistakes in an ESL student's work that can make it difficult to understand what meaning is being conveyed.
Usage mistakes, like grammar mistakes, are not particularly susceptible to eradication by direct correction. And like grammar mistakes they will eventually disappear, particularly if the student reads extensively in English. However, the mainstream teacher is advised to alert an ESL student to usage mistakes in the way he or she conveys a meaning that is common or integral to the subject. For example: "The dictator was thrown over (overthrown) in a people's revolt or
* There is a gray area where usage shades into grammar, such as in the choice of prepositions. For example: "I'm good at chess." is standard English, so is "I'm good in chess." a grammar error or a usage error?
Of course, a student may turn in a piece of written work that contains no mistakes of mechanics, grammar or usage, but is a long way from meriting a good grade. This is usually because the student has not understood or complied with the writing task, has given no thought to organization and structure, has made no effort to string sentences together in a coherent way, has plagiarized, and so on.
Most mistakes of mechanics, grammar and usage will disappear automatically as the ESL student becomes more proficient in English, so mainstream teachers need not focus too much attention on them. However, it is a primary task of the mainstream teacher to help ESL students (indeed all students) to improve in the more fundamental aspects of writing well, as listed in the previous paragraph. This applies particularly to subject-specific genres such as lab reports, persuasive essays, critical assessments of historical figures, etc.
There are many more examples of typical English-learner mistakes (including mistakes in spoken language) on the web page entitled Language words for non-language teachers. You may also wish to look at the page written for learners about writing mistakes and how to avoid them.