Cancer After Superficial Mole Removal?

Incompletely excised or lasered moles can grow back looking atypical. The key is to have the original specimen biopsy and if the pathology indicated benign nature of the lesion, then subsequent residual mole can be monitored.

Moles are not supposed to be removed by laser.  Lasers were designed for pigmented patches or sun damage.  The general consensus is that a mole needs to be removed surgically and sent to the laboratory for analysis.  I understand why you are concerned about the mole and what is left.  I recommend seeing an experienced board certified dermatologist who understands both cosmetic and medical dermatology.

You are not at any greater risk for cancer having had the mole removed by laser.  If you do happen to develop cancer in the residual mole (most moles never become cancerous) you will notice some change to the area.  The scar will not hide the cancer and will not cause the cancer to spread under the skin.  However, keep in mind that moles can return, and any evidence of recurrence does not mean it is cancerous.  If that were to happen, have a dermatologist examine the area and possibly test it with a biopsy. 

I just posted another answer on exactly this topic. I agree with your concern about difficulty monitoring the root cells of a mole that may be left under the surface after laser mole removal. For this reason, I disagree with using this method to remove moles at all. I prefer a small shave biopsy and sending the mole tissue for pathologic evaluation. Unfortunately, trying to "melt" away a mole for cosmetic purposes does leave you at some risk. It's hard to have it both ways.

A benign (good natured) mole usually stays benign, even if it was not removed completely. As you seem bothered, I would recommend to have the mole emoved completely by an excision a have it sutured cosmetically.   Naturally, the specimen sould be sent to the lab.

If the original pathology showed a noncancerous mole, subsequent biopsy of the area when it returns can look "dysplastic"/cancerous under the microscope. The location and pathology should be well documented and the information relayed to all cosmetic physicians you see

This is a fantastic question. Unless you saw a dermatologist who was certain there was no malignant potential in this "mole" you had treated, you do stand to risk potential masking of a malignancy forming in the remaining cells. This is likely a low probability, but this is why dermatologists hardly every use a laser to remove melanocytic lesions, without first doing a biopsy.

A laser which would rid you of a mole, by definition is ablative. This would mean that there would not be any tissue to send to the pathologist.
It is standard procedure to perform a small biopsy before the laser is used. You might check if that was done. Otherwise, the dermatologist must have been very confident that the mole was benign.
This underscores the danger of allowing lay people access to lasers unless they are under the direct supervision of a physician.