Is it a major problem if our bank does not complete the checking of customers on the 314a's within the two week required period for a few of the requests?
We may have 10 or 12 requests out of 52 weekly requests during an entire year that were completed beyond the 2 week period. ??

Yes, it could be. If you've got 10/12 out of 52, that's a 20-25% rate and could be considered by an examiner as a violation. This will be covered by them in the BSA examination.

The FFIEC manual says we "must" search and report within the 14 days. I'd be very nervous about that rate (20-25%) of non-compliance come audit time.

103.100(b)(2)(i) Record search. Upon receiving an information request from FinCEN under this section, a financial institution shall expeditiously search its records to determine whether it maintains or has maintained any account for, or has engaged in any transaction with, each individual, entity, or organization named in FinCEN's request.

Concerned - yes. Since you are required to report within 14 days, it is a direct violation of the Bank Secrecy Act. I have never seen direct violations treated as "no big deal", epecially with that type of error ratio.

This is a law enforcement statute, not some puny little consumer protection law. Your regulator could and perhaps should make that level of laxity the basis for an enforcement action.