Which of the following should be included as a bank error adjustment?

The inclusion of a deposit that was recorded incorrectly as a bank error adjustment is appropriate because it directly reflects a discrepancy between the bank's records and the company's records. When a deposit is recorded incorrectly, it implies that the amount recognized in the company’s books does not match what was actually deposited in the bank. This requires an adjustment to ensure the financial statements accurately reflect the true cash position.

In contrast, a transfer from one account to another generally isn't classified as a bank error. This operation is typically a normal banking transaction, and unless there’s a mistake made in the transfer itself that leads to erroneous balances, adjustments would not be needed.

A correctly processed payment also doesn’t require an adjustment, as it has been recorded accurately and the bank's records correspond with the company's. This clearly documented transaction should align without any need for correction.

Lastly, delayed check clearance is a timing issue rather than an error. The bank may have not processed the check yet, but it doesn't reflect a mistake by either the bank or the company that requires an adjustment. Thus, recording an adjustment for a delayed clearance is not necessary since it is a known factor in accounting for outstanding checks.