However acceptable some English grammar usages have become, synesis (notional concord), split infinitives, ending a sentence in a preposition and the improper use of who and whom will cause problems in some circles.
It is always wise to get these right, at least as they are perceived to be correct by many.
It never hurts to use acceptable grammar unless you want to give the impression of one whose grammar is lacking.
Commonly condemned usages are:

• Synesis defined as "A construction in which a form, such as a pronoun, differs in number but agrees in meaning with the word governing it, as in If the group becomes too large, we can split them in two.
  "
• Splitting an infinitive.
  To boldly go where no man has gone before.
  
• Ending a sentence with a preposition.
  That is the sort of nonsense I will not put up with.
  
• Using "none" as a plural noun.
  None of them were quite ready to be displayed in the curling club locker room.
  
• The use of "who" as the object of a verb or preposition where "whom" is correct.
  Who did the provost direct to remove the badger from the auditorium? Who did you receive the holiday collection of industrial adhesives from?
• A pronoun in the objective case after a comparative with "than" or "as" (sometimes called an elliptical reference): He is even more scrofulous than me.
  She is just as revolting as him.
  

A learned audience will not be impressed by correct grammar but may well be swayed by errors -- real or perceived -- which are regarded as non-standard.
It is far more important to make sure that subjects and verbs agree, that parallel constructs are truly parallel and that all words are correctly used.
If one's purpose is to offend and shock, however, the above should be ignored.
Other common errors are:

• Verb pair confusion: lie/lay, rise/raise, sit/set and fall/fell.
  
• Sentence fragments and run-on sentences.
  
• Mass nouns and count nouns
• Subjunctive usage
• Lists and coordination
• Misplaced modifiers
• Dangling participles

The exercises in SAT, ACT, TOEFL College Prep English practice text explains these at length with many examples and quizzes.
The examples used are never prosaic or quotidian.
Examples: 1.
Would _____ever the statuary director designated, please replace Prometheus' sword and remove the kangaroo? 2.
Would _____ever put the Jello on the table of the last supper tableau please return the fish?