I've experimented with panoramas rather a bit, starting quite a good length of time before the advent of digital imagery. The key to a fairly seamless panorama is that 'center of focus' mentioned above, rather than the center of the camera or the mounting point to a tripod. Light passing through a camera lens 'inverts' as it is focused; you've seen this if you've looked through some telescopes, particularly simple two-lens telescopes, when you've seen an upside-down and backwards image in the eyepiece. Where it makes that 'flip' is the center of focus, and it is different for each focal length lens.
Digital imagery and manipulation software make it somewhat easier to create a panorama, and the best work still takes that center of focus into account.
This photo is from October 2005 in Lake Chelan, Washington. I used a flash mounting bracket to off-set the camera in relation to the tripod mount, putting the center of focus directly over the pivot point of the tripod. It's two frames put together into a single image, and in my case I did not use automation to achieve the compositing.