Mike, you may find this interesting:
The first frame I built was without a jig and free hand in a bike stand. Pinned the main tubes and the triangle was only 3mm out of alignment. The second frame I did the same way, but much more careful and it was out by 2mm. Either one was not enough to affect the tracking of the bike when ridden. This last frame I did in a jig and it was 5mm out of alignment! Not sure what the heck happened, but I spent a lot of time getting 2mm of movement out of it to bring it back into compliance of plus or minus 3mm.