Let's keep going with the Inventor John example.

Suppose all of John's patents are granted.

At this point he now has three patents; a nonprovisional claiming the original furnace idea, the C-I-P covering the improvements to the furnace, and the divisional patent covering the air conditioner.

A few months after the air conditioner patent issues, John sends the air conditioner plans off to a development company. During the process of manufacturing the air conditioner, the company realized that something wasn't quite right. John is frantic. Luckily he knows how to fix it, but his patent is wrong! In his haste to file the divisional application, John didn't quite communicate the methods correctly.

So now what? Should he file a new patent? Or will the USPTO take amendments after the patent is issued?

The solution is for John to file a reissue of the patent.

Reissues may be used when the claims or specification of the original patent are not quite right due to an error made without any deceptive intention. The result of the error is that the patent must be deemed wholly or partly inoperative or invalid. The error might be a defective specification or drawing or a patent practitioner's failure to appreciate the full scope of the claims. 

A reissue filed within two years may even be entitled to broader claims than those in the patent application. 

If the reissue is approved, it will simply replace the earlier filed patent and expire when the earlier filed patent term was supposed to. Nothing is gained, but nothing is lost either (except the money it will cost to file the reissue). 

An alternate method for correcting errors in an issued patent (whether on the part of the Patent Office or the applicant) is to use a Certificate of correction.  These may be used for minor mistakes that do not involve adding in new matter or that require a reexamination.  Filing a reissue is advised to correct any mistakes that are not correctable by a Certificate of correction.