When learning anything about the Russian army, particularly in the second part of the War when they had the Germans on the run all we hear about is the mass rape and how drunk they were.
I always fail to see how an army who acted like this was so successful, and surely they could not have been well trained given the circumstances Russia was in.
Depends on the unit.
Any given army in any given theater is always going to have some form of bull pen for the folks that simply are not soldier material. Someone has to drive trucks, someone has to cook, and clean, someone has to maintain vehicles, someone has to cut the general's hair. There are plenty of non-hazardous guard details because when you have thousands of miles of roads, rails, and communication cables to account for, someone's probably got the idea that they could steal them.
In the case of the Soviets invading Germany near the end of the war there was a certain level of laxity regarding order in the ranks. While there was order to be maintained to a certain extent after telling the soldiers for years about the decadent Germans and the usual lines of propaganda suddenly turning them loose on the German countryside wasn't going to end well no matter what you did. You were talking about a country where your average citizen didn't know what margarine was, the only machine they'd ever interacted with was probably either a train or a tractor, and where staple foods typically consisted of the bare minimum to keep them alive and fed. Germany was like a stuffed pig for them.
All the training in the world wont help it when your average officer won't tell their subordinates no and their subordinates have been fighting in hellish circumstances with often maddening casualties every step of the way.
So while it is kind of a non-answer when you ask how disciplined the Soviet army was in WW2, I answer, "as disciplined as it needed to be."
I don't have time for an in-depth response but it's worth noting that, according to Anthony Beevor's Berlin, most of the cases of ill-discipline were attributed to second echelon support units. So the hardened formations that did most of the fighting were probably the best trained and disciplined. Then their comrades would rock up on the supply train and have themselves a 'good time'.
That said, unit discipline in the Soviet Army may generally not have been up to Western standards. Beevor also records instances when soldiers would simply dump their small arms in a large haphazard pile when making camp. But given the post-war myth-making I find it hard to know how much weight to attach to such stories.