I have a LA2, and have used it a lot. I cannot fathom how shot and powder would get mixed together like that in the form of some sort of machine defect. If it is that machine doing it, something is very wrong.
What does happen with many reloading machines sometimes, is when they are new, things don't flow completely. They have a break in time, if you will, before things will flow smoothly and completely.
It's common for powder to get hung up in the drop tube, shot however seems less likely because of it's weight. It isn't unheard of from machines like that to have a light coating of grease or oil on the parts that might be just enough for a few balls to stick in the drop tube.
I would try to rule this out. One thing you can do, is give it a tap after you've dropped whatever to make sure everything has passed the dropped tube. It could be possible that a little bit of powder is getting stuck, then push out with the shot, and a little bit of shot is getting stuck, and push out with the next powder.
Meanwhile, the LA2 is a great machine in my opinion. Great way to get into shotgun reloading on the cheap, and I've been able to do a lot of different kind of loading with just the one kit. You may find that it's not the most straight forward. While other high end machines, like MECs, allow you to dial in all the setting precisely to get the results you want, the LA2 requires you to "feel" things out. Getting a great crimp often relies on how much pressure you put into the pre crimp. Too much and you've ruined your crimp.