The "silver tape" you are referring to is foil tape. That is the only thing needed, no "caulking". People always think that pipe has to be "sealed". That is not the case at all. You have a forced exhaust system.
Probably what is occurring, is that you are getting smoke entering the house from a window or such from the outside. Kind of like car exhaust coming back into the car from the vents. Instead of checking for leaky piping, I would check for leaky windows. It is normal to smell a burning stove occasionaly.

Thanks Xanndra, I knew you would have some type of answer. I already checked the basement and first floor windows from the inside (by cracking them open) and out. The smell is not coming in through that way (I can't smell any smoke, only clean air).
I also "bumped" the end of the vent pipe towards the stove. The pipe moved in about 1/4". Does the vent pipe have to be flush against the stem from the unit to seal properly?

Pellet stove pipe is a double-walled pipe that is very similar to B-Vent pipe. The major difference in the two, is that pellet stove pipe (L-Vent) has a stainless steel inner liner, whereas the B-vent has an aluminum liner.

There is a special connector that hooks up to the stove (made by the pellet stove pipe manufacturer) that is designed in such a way that the inner wall of this adaptor goes into the inner wall of the collar on the stove, thus assuring a tight, non-leaky fit. There is a possibility that the installers did not use the proper connector on the back of the stove exhaust. If that is the case, then yes, you may be getting some spillage into the room. If you have some "give" in the pipe at the stove collar, I would disconnect it and see if it is fitting tightly. Also, check to see if the gasket is missing from between the two liners (it looks like a soft piece of rope). If it's not fitting right, I would call the installers back and make sure they used the proper stove adaptor with the gasket. Now, some models of stoves do not need this special adaptor. On these stoves, any length pipe will fit snugly without the stove adaptor, but still needs the gasket (the gasket is installed with each piece of pipe). I cannot remember if the P68 needed the adaptor when Dura Vent brand pipe was being used. Some models of Harmans needed it, some did not.

My opinion: The problem is in the installation and not the stove.

Thanks. The dealer has been great and we're trying to figure out what happened. My only question is why did it occur after almost three days. Could the vibration have shook it loose?
When the distribution fan is on, the air blowing into the room smells pretty clean.
I'll keep you posted.

Possibly the vibrations have loosened up the pipe or a connection somewhere.

As far as the distribution fan goes, it only moves heat from the stove. It would not have anything to do with the exhaust fan so it should be clean.

Xandra;
I checked the back of the stove as it started up. I noticed wisps of smoke coming out near the bottom of the vent clean out. There's a lever down there, with the tape around it. Is there any special seal or cap for the bottom of that pipe?

Sorry, I can't answer that question for you since I don't have a unit in front of me to know what you are talking about.

Most manufacturers recomend using high temp silicone caulk on adapter piece of pipe to stove. At least Harman and Quadrafire has it in their installation manuals. I kept getting smoke out of my pipe joints after cleaning my pipe this winter and didn't get it to stop until using high temp silicone on the adapter and on the joints. The silver tape created too much of a toxic oder. I wound up taking it off and using the silicone.

I just had a p68 installed and also got a smoky smell. I found the pipe joints were not cauled with the silicone that well. You could see a brown discoloration on the silicone where it was leaking. I held a lighter up to the pipe joints and could see where air was coming out. After recaulking he smell is gone. You can smell a slight smoke odor at time but i think that is normal.

This response is pretty late but here's my opinion after having 3 pellet stoves over the years, and now a Harman P-68:

If a "t" was installed at the back of the stove where it went up 6 feet, it should have a stove adapter between the "t" and the stove. This adapter has a fiberglass rope seal inside it. The adapter should be RTV siliconed where it attaches to the stove, pushed in tight, and attached to the stove flue with sheet metal screws so the adapter can't loosen/leak.
If that has been done correctly, then check the removable part of the "t" (the cleanout) and make sure that it also has a rope seal and is tightly connected and either siliconed or wrapped with metal tape. All inside connections must be sealed.
I've installed all three of my stoves (Jamestown Baby Bear, Harman Advance, and the p-68) and never had a smoke leak in the house.
I also learned that things work much better with at least a 3' rise on the outside of the house.