You picked a complex subject there Mike as doors require "tweaking" in many different ways.
First is diagnosing the problem which there are many possibilities. Sag/settling (door and frame), hinge binding, hinge wear, warpage ( twisting, cupping). kick out/kick in, shrinkage/expansion.
So now we have the terms (probably missed a couple) we have to know the corrective measures or if replacement is required, and yes sometimes you just have to rip them out and put a new one in, especially if you have severe cases of warpage or kick in/out. This could be the door or the casing with these problems.
The first thing to check is if the jambs (frame) are plumb(vertcall) in both axis and is it level (Header and sill) these are easily checked with a framing square and level. Remember there are two planes to check in the vertical the edges (where the casing (trim) gets fastened and the inside flats (sides where the hinges and strike plates go).next is if the door square and free of warps or cups.
Sag:
Generally this is from stripped screws, hinge wear or a poorly constructed or door.
If it's stripped screws there's several ways to do this. longer screws, oversize screws, drill amd plug, wedges ,shave down a shim or piece of wood to a taper larger than the hole then apply glue and tap in with hammer let set then trim with chisel. Or use plastic wall plugs in a pinch.
If it's the hinges you could replace them or use hinge tools to reset the gapping or tighten the ferrules.
http://shop.justdoortoolz.com/product.s ... tegoryId=7Alternatively you can use the method you posted
Now to the actual door sagging.
Usually this requires replacement if severe but the trusty hand plane is by far the simplest method to correct this. Do not plane the material from the latch area as this will alter your backset! Take the excess from the hinge side and re-mortise the hinges if necessary. You can safely plane any of the four corners.
If it's say a two or six panel door where the rails and stiles have loosened over the years you may be able to disassemble or partially disassemble then re-square and glue the carcass and save the door (do not glue the panels to the carcass). This is a little work heavy and I'll skip the method required. You can find out about panel door construction on the web. Occasionally what appears to be door sag is in fact a result of house settling and the building shifting out of plumb level use your level and square to verify and if necessary remove the door, jambs and casing and re-install plumb and square ensuring you don't get binding on the floor. when removing old casing a good tip is to use a utility knife and score along the edges preventing paint tear-out on the walls.Another is to pull the nails out through the back of the trim to prevent tear-out.
Qyick fixes include shifting the strike plate or hinges up or down and of course planing.
Hinge binding:
There's several ways this occurs; most commonly lack/loss of plumb or warpage in the jamb/door excessive inset/mortising either in depth or vertical alignment on either of the two axis. twisted hinges due to poor installation/mortising. check to make sure the hinges are flush with the jamb/door edge and are inline with each other on the door and casing. Verify the jamb/door is plumb and free of twists or warps adjust the hinges laterally to make up for minor variances.
Kick in/out:
This is caused by kicking/forcing the door or by jamming objects in the way of the door when trying to opem/close it. It can also be caused by warped doors or jambs. Indications are gapping at the top or bottom strike side or uneven alignmnet with the door stop. Replumb jambs where necessary replace doors if they are warped (sometimes you can cheat by removing the door stop and reattaching it in alignment with the door) Steel exterior doors may be straightened by flexing the door in the opposite direction but usually the integrity has been lost and replacement is necessary at some point.
Shrinkage and warpage:
As you pointed out these are usuallyseasonal problems and the trick is to give yourself as much play as possible without having a sloppy installation. Options may to find a door with a more stable constuction whether wood or some some other material.
The key to any door repair is to diagnose the problem and apply the suitable remedy. Unfortunately the tricks of the trade tend to require years of experience but the knowledge is out there should you choose to search for it. I've been a carpenteer for 35 + years and I still pick up new tricks here and there. so don't get frustrated and feel free to ask me any questiopns you may have i'm here to help.
I hope this post makes sense if not I'll try to clear up any questions anyone has.
Cheers: Mike