The sound of the prepositionof is similar to the sound of 've--the shortened form of the helping verbhave. As a result, of is sometimes misused in contractions.

Have often functions as an auxiliary verb (or helping verb). In speech and informal writing, the contracted form 've is sometimes used with the verbs could, must, should, would, may, and might.

Of is a preposition, not a contraction. 

Also see the usage notes below.

Examples:

• Jed could have tried harder to help us.
• Jed said, "I would've tried harder if I'd known you were paying attention."
• Some of us must have been watching the game when the burglars broke into the house.
• "If the Mets would have given him two more runs per game, Seaver would have won 20 games by the end of August. But that was one of those would've, could've, should've scenarios."
  (Josh Rosengren, Hammerin' Hank, George Almighty and the Say Hey Kid: The Year That Changed Baseball Forever, 2008)
• "The planning of the fly was an application of pure intelligence, morals not being concerned. Not one of us could have planned the fly, not one of us could have constructed him; and no one would have considered it wise to try, except under an assumed name."
  (Mark Twain, "Thoughts of God," early 1900s)

Usage Notes:

• "Mr. Wood, my English teacher, is always telling us that 'there's no such thing as must of, should of, could of, it's must have, should have, could have.' Mr. Wood says stuff like, 'The day you all get that simple little fact into your tiny little heads is the day I can retire a happy man.' Well, this is all very well and good, but he doesn't need to be moaning on to me about it."
  (Hayley Long, Lottie Biggs Is [Not] Mad. Macmillan, 2009)

• "When we speak, we slur these phrases so that they all sound as if they end in of, but in fact all of them end in have. Their correct forms are may have, might have, must have, should have, would have, and could have."
  (Susan Thurman, The Only Grammar Book You'll Ever Need. F+W Media, 2003)
• "Some writers use of for 've deliberately to add flavor; should of and I'd of have a drawled look that the more clipped should've and I'd've lack. Ring Lardner and John O'Hara often used of for 've, and it is unlikely that either did it from ignorance."
  (Edward Johnson, The Handbook of Good English. Washington Square, 1991) 

Practice:

(a) One _____ us made a mistake.

(b) It must _____ been you.

(c) "She was one _____ the few gentlewomen I _____ ever known, and has remained throughout my life the measure _____ what a human being can be."
(Maya Angelou, I Know Why the Caged Bird Sings. Random House, 1969)

Answers to Practice Exercises

Glossary of Usage: Index of Commonly Confused Words