Re: forearm of stock touching barrel
The key here is consistency.
If a synthetic stock is contacting the barrel in a particular spot, then yes the barrel harmonics may be affected. However if the point of contact doesn't change, then neither should your shot placement. You would still get consistent groups. Where abnormal contact with the stock comes into play in regards to affecting consistency on target is when you have a wood stock, as oli pointed out. Swelling and contracting in the wood due to temperature and humidity variation will affect a change in pressure at the stock's point of contact with the barrel resulting in changes in barrel harmonics and noticeable changes in shot placement. However in this case the changes occur slowly, usually resulting in a shift in your scope's zero between range trips. Even with a wood stock, you wouldn't likely notice any significant variation during a single range trip.
Bedding the action/barrel will help eliminate one variable, but there are others to consider. Aside from shooter fatigue, barrel thermodynamics can be the most significant attributing factor to sporadic shot placement and scattered groups. It's not just that the barrel heats up either. It's that the barrel is constantly heating up and cooling down between shots and not always in a consistent way. Some parts of the barrel will heat up and cool down faster than others resulting in irregular temperature variation along the bullet's path. This has a direct impact on how the bullet behaves when it leaves the barrel. Fire a single shot and the receiver heats up, then the heat travels down the barrel. When a second shot is fired before the entire weapon cools down to ambient temperature the bullet is traveling through a barrel that is a different temperature, with different rigidity and harmonics than on the first shot. As you continue shooting, these factors can progressively degrade your consistency on target.
Here again, the key is consistency. Establishing a consistent shot cadence, or the amount of time between shots, that works for your rifle will help to improve your consistency on target. Your cadence should be tailored to the intended use for the rifle as well. One school of thought here is to fire a string of shots in rapid succession. This will heat the entire barrel in a relatively even pattern and not allow time for cooling between shots. Knowing how your rifle performs under these conditions would be useful for hunters or for scenarois where immediate follow-up shots may be required. Another school of thought will come into play when shooters are striving for tiny groups on paper. For the absolute best results on target, a rifle will never perform better than on a clean, cold bore shot. This type of shooting can require a lot of patience as it may call for upwards of 15-20 minutes between shots in order to allow the barrel to cool back down to ambient temperature. Running a bore snake through the barrel between shots will also help remove any fouling that could cause a variation in your shot placement. This takes a lot of time and patience, but is a great way to tune your rifle and ammo for consistent sub-MOA results on target.
...just a couple things to consider...
