A big problem with dot sights is that they are VERY sensitive to the shooter's cheek weld which changes the shooter's eye's alignment to the optic, the dot's, and gun's orientation on the target which moves the POI sideways,up-down and even circular.
No offense, but this is incorrect. Although it is a problem with many other optics, it is not the case with an Eotech. In fact, this aspect is one of the major benefits of the Eotech system.
If you check out the Eotech website there should be some info explaining this. Basically, no matter how off center the reticle appears, your shot will still hit POA. This is a major benefit if for some reason the optic is damaged (ie cracked glass).
ETA: Here's the link explaining this concept. http://www.eotech-inc.com/page.php?id=8
So, OP, I wouldn't factor that as a possible problem. As long as you see the reticle, the bullet should impact wherever you put that dot (assuming it is zeroed correctly).
Also, you probably aren't going to get amazing long range groups with an Eotech. I often do better with anything past 50 yds using the irons. I'm not saying that's going to be the case with everybody, but it's the case with me. The Eotech's main purpose is quick target acquisition in CQB. It's just not made for precision. Of course, with a bit of practice, I have faith that you will improve. It took me a few trips out with my 512 before I started getting the accuracy out of it that I wanted.
If you really want to see the benefits of speed that the Eotech offers, head out to the woods, set up a bunch of coke cans in different places and do some "speed plinking." You will see that the Eotech is an amazing tool in terms of fast follow ups and speedy target acquisition.