If they have Alerts & Workflows you could set up an event to monitor any records written to IM_ItemCost that are missing the TierType. if you immediately knew the time the record was written you could narrow down the transaction that created it. If the bad record occurred in a sales journal update you could try and re-create the transaction in a test company.
Alternatively, you may be able to get a similar result by installing SQL and creating a linked server. You could create/replicate the IM_ItemCost table in SQL and have it update periodically. Have a trigger on the IM_ItemCost table to monitor for newly added bad records. Have a log file that records the date and time the records were discovered. Because of the sync, this would be an inexact science but you could get a range of times the bad record was added and may be able to narrow it down to what transaction created it.
Seems like a lot of work but if the client is one you want to save it may be worth the effort.