Mistakes I came across are as follows:

1 Use 和 to join clauses

When joining two clauses, "and" (or other conjunctions such as 'but') is necessary in English while "和" should not be used in Chinese. 

2 Use 是 between the subject and the adjective which describes the subject.

Actually we never use 是 between the subject and the adjective which describes the subject, unless we want to emphasize that it's true.

For more detailed explanation, see http://www.italki.com/entry/347334

BTW: Sometimes the 是 between the subject and the NOUN that describes it can also be omitted.

e.g. 今天(是) 星期三. 今天(是)15号.

3 Use 很 only when he wants to say 'very'.

e.g.

它难. Actually this sentence sounds so awkward that Chinese people are unlikely to understand it during conversation. Instead, we always say 它很难.

Some people believe that 它很难 = It's very difficult and 它难 = It's difficult. They are wrong.

In fact, 很 doesn't normally mean a greater degree unless it's emphasized in speech.

See also http://www.italki.com/entry/162678

我发现很多外国人在说话的时候会漏掉“是”这个字，比如我上次碰到一个人说“我的眼睛不蓝色”和“他同性恋者”，这个“是”很容易被漏掉！可能是因为他们母语的语法造成的吧，我发现很多中国人学英语的最大毛病也是这个原因，由于母语的语法受到干扰，出现过很多中式英语！我觉得这是一个很难改掉的毛病，这需要时间！

l  found  that  when  foreign  people   speak  Chinese,they  often  ignore "是“，l  do  not  know  the  reasons,maybe  just  because  of  their  native  languages'  grammar,and  l  know  the  biggest  problem  for  Chinese  people  of  learning  English   is  that  we  often  follow  Chinese  grammar,then  it  appears  Chinlish(Chinese--English),for  example,some  people  would  say "l  think  l  will  not  come  tomorrow" ,this  is  a  obvious   problem,and  we  have  a  long  way  to  go  in  order  to  drop  such  a  obvious problem!

@Alan That's the author whose book I mentioned = 这是写了我之前谈过书的作者

这就是我之前提到过的那本书的作者-you are not wrong, but it  is better. me, OCD, slightly, I guess.......

I can't help correcting the sentences when nobody does 

@ninapengxin： 我对那有兴趣。在英语，‘是’跟形容词和名词用，但是在汉语它跟名词用。在英语，‘同性恋者’和‘蓝色’是形容词，所以也许他们觉得在汉语他们也是。

@jane：谢谢。我会记得那个。

@沙曼沙曼：谁学习的汉语经常被告诉每个字跟’个‘可以用。那不对还是不自然的？

很多人不太会用中文的量词！比如中国人会说“一条鱼、一本书、一张纸”，很多人学习中文时不会用量词，他们把所有的东西都用“个”来形容。比如“一个鱼、一个书”等，这很奇怪啊！！