I made an error with the number of shares owned at end of year and start of year on K-1's for my small business. Am wondering how critical it is to correct the problem

The number of shares owned will not affect your income or deductions, so you do not need to file and amended return.

Will this trigger IRS to want to investigate whether we sold shares?

At worst the IRS will send you a letter asking for clarification.  Even that is unlikely.  If you have the correct number of shares at the end of the year for 2021 and you carry that forward you will most likely have no issues.

I made an error on number of share owned at end of year.  I typed 100 instead of 1000.  Do I need to amend 1120S?  Single member S corp.  Please help.  I efiled the return already

The number of shares does not show on your tax return and it will not affect your tax, so you do not need to amend your return to report it.

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