I like seeing this thread as it begins to get the Russian side thinking of strategies and tactics for how the game currently is.
Historically, the Russians were weak in the spring and early summer of 1942; in some ways even weaker than in the opening days of 1941 in terms of unit skill. The game now generally reflects that. As a disclaimer, I have not had a chance to work in a campaign as the Russians yet under 1.05, but this comes from observation, etc.
To me, some important things the Russians must look at is trying to rebuild a cadre of quality (for Russian) units to use at decisive points and times against the Germans. Until then, the Russians should keep them out of sight and away from harm and continue to work on increasing that pool of units. Examples of these units include guards, mountain, cav corps, and as you get them to come on line, tank corps.
During the winter, the Russians not only want to hurt the Germans as much as possible, but also use it to build moral and get as many units promoted to guards as they can. This also includes tank brigades as well. As soon as a unit hits guard status, they should usually be withdrawn to rest and be brought up to full strength. Tank brigades need to be removed immediately to be saved for being formed into tank corps.
As some others have mentioned, defense in depth and having deep reserves is the way to go imo. Good AP management is a must as well since you want to be able to form new units as needed (you should actually have a trickle of new units in a pipeline every turn until close to mud in the fall of 1942 or until the German appears to have shut down offensive operations). The only way you can really lose the game is put yourself in a postion where the Germans have removed enough counters that you can't defend. (This assumes you did ok with evacing industry).
The other thing I have seen is the Russians sit a bit too calmly on the total defensive and simply react to what the Germans are doing (usually in the south). This sort of plays into the German hands as he wants the front quite in many spots while he concentrates his best units and tries to wipe out a large chunk of your army. To me, I would consider having a shock army (or two) in reserve for offensive operations. The idea is once the German becomes committed in the south, you start hammering the line someplace else. You simply can't go toe to toe with the best of the German army in the first part of 1942, so don't even try it. Instead, try to limit the damage, but don't be afraid to give ground. In 1942, he has to beat your army and get a lot of counters gone. On the other hand, the German army breaks when he gets knocked down to a certain amount of infantry. You need to figure out how to cause more losses to his infantry. It doesn't have to be anything fancy, but stretch his line, beat on his infantry and make him commit more resources to defending where you are attacking. Make him be out of static so his attrition will be higher. If he shows up to counter what you are doing in sufficient force, fade away. You can't risk your good units yet because you simply don't have enough of them. Consider rotating units depending on what happens so you can increase your pool of good units.