In addition to using the Epstein System with my older son, I spend a significant amount of time working with current and former clients of Mike Epstein's. As a result, I have a good sense of the strengths and weaknesses of the Epstein System.
Strengths
The biggest strength of the Epstein System is its simplicity. The limited number of concepts and drills makes it easy for people to get started and to make quick progress.
Weaknesses
Unfortunately, the Epstein System has a number of weaknesses, many of which outweigh its strengths.
Accuracy
There are a number of problems with the accuracy of what Mike Epstein teaches as being representative of the high-level swing.
Squishing The Bug
While Mike Epstein correctly rails against Squishing the Bug, many of his drills put the hitter in the position of Squishing The Bug. That creates the same problem as Squishing the Bug; it restricts the rotation of the hips.
Weathervaning
While Epstein's concept of weathervaning is generally right, the problem is that you have to do that while maintaining one's Alignment, and that means focusing on the front arm, the front shoulder, and the barrel, not just the front elbow.
Adjustability
Mike Epstein spends very little time talking about the concept of Adjustability, and what he does discuss is generally wrong, largely because Ted Williams also got it wrong. For instance, good hitters adjust up and down in the strike zone by tilting forward over the plate, not back toward the catcher.
Rotation
I have worked with a number of Epstein clients who have sub-optimal hip rotation. This is usually due to their trying to rotate their hips by driving their back knee down and in. However, in a good swing, what the back knee does is the effect of what the hips are doing. It's quite possible to drive the back knee down and in and not produce any significant rotation of the hips.
Bat Drag
Mike Epstein doesn't seem to understand the problem of Bat Drag. As a result, when he and his instructors talk about slotting the back elbow, they don't seem to understand that there is a right and wrong way to do that.