This is another comedy technique from the checklist found on page 186 of Creativity For Entertainers Volume Two: Creative Techniques and Tools.
Mistaken identity is when a character uses an object in the wrong way because they don't realize what it is. The audience however knows the object's true identity. For example, when I was in college I saw a comic opera where the cowardly villain was challenged to a duel. He substituted a banana for one of the dueling pistols. His dimwitted opponent picked up the banana without looking at it and vainly strutted around brandishing it.
In the opening scene of the 1965 Disney film "The Monkey's Uncle," a chimpanzee gives a banana to the judge in a courtroom. When the spectators start laughing, the judge attempts regain order by pounding his gavel. He picks up the banana by mistake and pounds it on his bench.
The mistaken identity routine that you may be most familiar with is banana/bandana. (You can read more about this routine on pages of Volume Two - 11, 77, 78, 103, 199, 355 Creativity for Entertainers Volume Two and pages 246-251 of Creativity For Entertainers Volume Three.)
The Top Ten exercise on pages 102 through 104 of Volume Two will help you create other mistaken identity routines using a banana.
When I have taught about mistaken identity in lectures I have used a cartoon by Smiley from the 1950's. It depicts a man setting his watch while looking at an old fashioned gas pump with a dial to register how much gasoline was sold.
I explain that to perform that gag today you would need to switch it by using props people can recognize. I suggest setting a digital watch while looking at some type of digital display. (You will find a chapter on Switching in Creativity For Entertainers Volume Two 110-124.)
Recently I had my own experience with mistaken identity. I glanced at the digital display on our stove and saw that it read 425. I thought I was late for an appointment that I was supposed to leave at 4:00 to meet. I began to rush to leave and then noticed a clock that said 3:45. What I hadn't realized is that the digital read out on our stove that normally displays the time was displaying the oven temperature because Carole was doing some baking.
That could be a potential clown skit. It would be difficult to set it up so the audience understands what is happening, but it would be possible.
Mistaken identity does not only apply to objects. People can also be misidentified. For example, in the classic fairy tale of the Brave Tailor, the tailor brags about how many flies he has killed. The king thinks he is referring to dragons and mistakenly thinks the tailor is a knight. So the king sends the tailor off to fight a dragon menacing the kingdom.
What mistakes would your character make in identifying an object or another character? How can you make sure that the audience knows the true identity? What would you do as a result of your mistaken identity?
You can read more about mistaken identity in Creativity for Entertainers Volume One on page 134 and Creativity for Entertainers Volume Three pages 250 through 251.