Please make sure that a log has a following information:
1. date of payment
2. invoice date
3. invoice number
4. invoice period of coverage
5. invoice total $amount
6. $ total balance of a contract

Please note.
If an invoice has a billing problem, and  you are working with a company in order to correct it, show this invoice on the log  too, but do not subtract it  from a previous balance, make a note instead, that this invoice is not paid, and a reason for this, highlight this line.
Please also show on a log an invoice replacing an incorrect one with its number.
In this case we will have all information in one place and it would be ease to find what month was skipped, what invoice has been corrected, and what invoice has corrections. We wouldn't need to shift all invoices and all related paper work while investigating a problem.

Also, please keep all records of your contacts with a billing department which made an error on an invoice. Keep all dates, names and other information. Staple all paperwork together and write on the top invoice number. This is very important to have while communicating with a company.