What is the difference between:
- "I did a few mistakes."
- "I made a few mistakes."
Are they the same or not?
My question is about the collocation: Can I use "made" for the word 'mistake' or not?
Do and make in this context are both light verbs†. Which verb works is somewhat arbitrary; you'll simply have to memorize which light verb goes with which noun, one by one:
give a hug
make a mistake
take a nap
do a review
have a swim
The correct light verb for mistake is make, and your phrase made a few mistakes is perfectly fine.
In contrast, do is the wrong light verb, so your phrase *did a few mistakes is ungrammatical.
†For more information about light verbs, see Huddleston & Pullum's Cambridge Grammar of the English Language (2002), p.290.
I believe personally that the proper way to say it would indeed be "I had a mistake." Think of it this way. You don't say "I made a take", however you say "I had a take". Or "I had a shot", so why when it is the opposite context that all of a sudden we put a "made" as opposed to "had"?
You don't say "I made a misfire in my car today." You say "I had a misfire in my car".