I don't think there is an exact answer here. Most of the issues you are talking about have more to do with the storage, age, time, and manufacturing of the lumber. So basically you will have a couple of people working at HD or Lowe's that contract out to mills or other lumber yards to get their pallets. Of course "older" lumber is cheaper. But you don't know how it was stored and climate/time of year factor into these things too. Leave some 2x4s out in humid summer heat and they are done in a couple days.
If you are getting a ton of lumber your local lumberyard or something like an 84 Lumber (which I use a few times a year) is a better bet. First their quality is almost always better and also they will drop off at your door if you hit their minimum. I order about 10% more than plans. This really isn't because of board defects but is more for planning defects or bad cuts.
Right when we get a pallet we do an inspection. If we think we will use the whole thing within a day or two we will bust it open. If not we work off the top and try to keep the straps on. It is inevitable that we will find a board with a crown or bowed. You don't take back every piece that has an issue - you don't have time for this and sooner or later a lumberyard would cut you off - this comment is for framing dimensional lumber like 2x4/2x6s and anything bigger you would be more stringent. What do we do with the slightly bowed or warped? We either hide them in places where it doesn't matter or cut them up for crosses.
Now I do sometimes receive a pallet and you can just tell right away that it sucks. In all of those cases I call up my rep and tell him the pallet sucks right away. Again you have to have a relationship with a place to do this. But he would usually spot me a discount and just ask me to snap a picture of anything that I can't use.
Some general tips for dealing with the big boxes (Menards, HD, Lowes):
- don't buy anything white. If the board doesn't have a yellow tint don't touch it. The cheap white pine they sell I wouldn't use for anything and it flakes at the ends when you try to nail into it.
- their employees are told to put the scraps back on top. It could be the case that the top three layers of any pallet includes scraps that someone else discarded. I have no problems throwing out 50 boards in a pile on the floor until I start seeing something decent.
- if you want straight and durable you are going to have to buy the highest grade that they sell in most cases. Most big boxes near me sell two varieties of #2 (pure white crap) and two varieties of #1 or premium. Sometimes and I will emphasize sometimes the worst grade of #1 is OK. This depends who is buying at your store.
- I usually buy my framing lumber with one of my older kids in tow. I will check it for twisting and vertical warping (if one board is warped chances are the one next to it is too). My son throws it on the floor and makes sure it lies flat. It is very normal that when looking for 30 2x4s we find 4 in our first 30-40 boards and the rest in the next 30-40.
- special note for PT. Don't buy any PT 2x4s that looked like they just came out of the pool. My HD loves to sell super wet PT. I have complained numerous times (along with several other contractors I know) and the lady that handles the fulfillments just laughs at us and acts like we are idiots. She has told me personally that PT is supposed to be that wet (it actually drips when you pick it up). So dumb she thinks everyone else is dumb. Two takeaways from this. You are at the mercy of those ordering at the store. And if you buy that wet PT it will warp and twist when it is drying - even if you get it to use.
- sometimes you will only find a good pallet in a certain length. I have been to HD many times and seen that all of the 96" boards suck. But walk over to the 104s and bam a good stack.
- they take anything back. The only thing you can waste at big box is your time. You can grab 30 twisted boards and bring them all back and they don't care.