-The rocket launcher is a pretty versatile weapon. Sure you have great range, but it doesn't have a high effective range [damage decreases over distance].
-The damage is good, but nowhere near compared to any of the demoman's weapons. Accuracy is perfect, it all relies on prediction.
-Never depend on crits. I'm not going to express my hatred of crits here (even if I get them).
-Sure, the Soldier may be slow at moving. That's why you have to utilize rocket jumping to its fullest potential - and if you do it right, you will lose little health and you can get buffs from medics and heal from med packs prior and after rocket jumping. (I use rocket jumping to get to areas faster, catch up to enemies, escape, etc).
As for the shotgun;
Great backup weapon. Couldn't ask for anything better. You usually will not have to switch to this because most of the time, your enemies are already dead by your rocket launcher. You can also preserve ammo from your primary by rocketing a 125 - 150 HP class, then finishing them off with a well placed shotgun shell. You can also use the shotgun to finish someone off in mid-air if you actually need to reload your rocket, as well as weapon heckling against compression blasting pyros.
Shovel:
You're better off using the Rocket launcher and shotgun. This is extremely useless for the Soldier, because he's so slow when you switch to it. There's no point of sneaking up to them with the shovel, you might as well shotgun them, or just rocket them.
P.S. to Soldiers who are bunnyhopping addicts with their rocket launcher: Do that to a competent Soldier, you will find yourself juggled, and eventually gibbed in mid-air. (I love when Soldiers do this to me, it makes it so much easier to kill them).
P.P.S. The most useful console command for Soldiers that will affect your gameplay is: cl_interp 0