If a participant properly rolls over an amount well within 60 days, but the company receiving the rollover does not cash the check for 4 months because the company did not realize it was a check (evidently thought it was a receipt), is the rollover still proper (can the check be cashed now as part of a "60-day" rollover)?

I don't think so. The IRS has been firm in that the 60-day period is absolute. I remember a PLR where the 60-day rule was clearly created and violated by the bank trustee's poor processing and the IRS still said too bad. The 60-day rule applies even if the problem created was beyond the control of the individual. You may want to look at the cases and PLRs on point.

Mr. Berke is correct that the rollover rules are harsh and stiff. You might want to rethink who received the check. Who is the "company?" If the recipient was a fiduciary of the qualified plan of the "company," or the custodian of an IRA, the check may have been delivered to the plan or IRA. That would complete the rollover in the required period. The rules require delivery, not reinvestment. But then the fiduciary or custodian would have to answer to why the funds remained uninvested for an unreasonable period. And perhaps the failure to cash the check for an unreasonable period would undermine the theory that the funds were effectively delivered to the plan or IRA.

This is really an operational issue. The individual should have a serious conversation with 'The Company' .The company must accept some responsibility for this. I have seen instances where custodians deposits the check and make a notation to show the actual received date, e.g. 'rec as of..'
if 'the company' does not make the individual whole, then this will not only be taxble to the individual, but will also no longer have the benefit of tax deferred growth.

I am sure 'the company would prefer to make good for their administrative carelessness, than to be dragged through an arbitration!!!

On the PLR issue, while PLRs give a good indication of how the IRS would treat an issue, they can be relied upon only by the individual to which they are issued and cannot be held as law- in addition, there have been several instances where the IRS has issued PLR with opposite decisions, even though the facts are the same