If the asset statements for a retirement plan do not have the assets in the name of the plan, what happens? What corrective actions must take place?

You have a problem and should contact the plan's attorney.

How many participants are in the plan? If they aren't in the name of the plan, whose name are they in? Is it a qualified trust? What have the 5500s reported? Auditor reports? 1099s?

I came into a situation after it was discovered that when the ER moved his Keogh profit sharing plan from a bank where it was trusteed to another financial institution, the receiving financial institution erroneously set up the transferred funds into "SEP IRA" accounts. The financial institution can't get its head around the fact that it made the error--so it's position is that the prior bank handled what is truly a SEP IRA erroneously as profit sharing plan. Nonetheless, we've filed a VCP application which has now been pending with no response from the Service for 6 months+, for failure of the Plan assets to be held at all times before distribution in a trust, as required by 401(a)(1)--as well as for the failure of interim amendments to the plan's documents since the assets left the bank. The correction proposed as part of the VCP application is to establish a properly titled account and transfer the "SEP IRA" assets to the properly titled account.

The situation I am dealing with is exempt from Title I of ERISA, so we have not also sought resolution also through the DoL as a trustee violation.

I think it depends on the degree of the error. If the account is titled as some kind of qualified retirement plan account but the name is just messed up, fix it and move on. If it wound up in an IRA, that's not so easy to fix - the custodian will want to do some reporting on the "distribution" when the money goes out, even if it was a mistake in the first place, and as noted, that might take more action.