Good counting controls have very little to do with AX at all. There are some AX gotchas, like the fact that the on-hand numbers includes Picked inventory. That means if you have an outstanding picker, say for 100 of an item, but you haven't yet removed that 100 from the shelf, you'll be counting inventory that the system isn't including in the on-hand, and thus adding 100 in error. And of course, good physical controls, such as not counting inventory that's on the dock but not yet received, or inventory that's on the truck already packing slip updated, as so not to count inventory that isn't part of your on-hand yet or anymore.
As far as counting errors, which is to say errors that result FROM poor counting and not corrections to inventory that are a result of proper counting, there are simple things you can do. This all assumes you're counting by hand. I don't see how you can do a count by barcode scanner and find yourself having to do it over.
Deploy your counters in teams of two, but NOT so that one can count while the other writes. BOTH count, and when they agree on a number, then they write. You want two independent counts on everything that agree. Second, follow up all teams and double check their first 20, 30, or 50 counts yourself. Some people just cannot count. And by that I don't mean they can't add or multiply, I mean they just cannot pay attention to details, and they double count, or miss items, or mistake part numbers, or transpose their answers, etc.
You have some idea of the accuracy of your warehouse on-hand, let's say it's 99%, which means you have an idle error rate of about 1% at any point in time. If you follow-up count a team and find 5 mistakes in the first 50 counts for that team, that's 10%! That team is generating more errors in your inventory by counting poorly than they could possibly fix by counting at all. Send them home. Counting poorly is almost always worse than not counting at all.
In my experience, the biggest mistake most companies make on inventory counting is to throw every employee on staff in the warehouse and assume that everyone can do it. If they don't know your product numbers, they're far more likely to confuse like products with similar numbers. If they're not familiar with the layout or physical controls, they're far more likely to count written-off inventory that should be ignored or count quarantined stock as if it were main stock. The pressure to get it done quickly often outweighs the need to get it done accurately.
The second biggest mistake companies make is to pretend they can do a controlled physical inventory all while shipping and receiving, that they can count with inventory in motion and keep it all straight. Most of the time, they cannot.