I'm an industrial engineer and geek out about Aldi frequently. Here are a few things I've noticed (and researched) which differentiate them from others.
-they have barcode on 5 or 6 sides of their products, and they're typically huge! They nearly never need to orient a product to scan it. Their scan speed is far faster than any other supermarket I've been at.
-if two products are very similar, they'll change the packaging in an obvious way. Blueberry and blackberry yogurt typically look very similar, but the lids are obviously dark and light purple at Aldi. They can glance down and count how many of each, scan one, then hit the number pad for the quantity. I haven't seen the number pad used extensively at any other grocer.
-they combine varieties (like flavors of granola bars) of product in the same box. This greatly reduces the shelf space required.
-depositing a quarter for a cart eliminates the need to pay people to collect carts
-they keep product the box from the manufacturer. This eliminates labor from unboxing and facing product.
-they don't have plastic bags. You can grab boxes (normally a waste stream) and take them home with you.
-they don't list a phone number for their stores. With as few as 2 people on site during the slow times, they can't afford to have anyone on the phone.
-their conveyor belt is far longer than most stores. You should be able to get your entire cart worth of groceries on the conveyor at once. This minimizes the slowness of people handing one item at a time to the next checker.
-They're big on turning inventory over. If they trial a product and it doesn't sell well enough, they have no problem simply not carrying it anymore. You can't always get everything set Aldi, but you can get 85-95% of items you need there.
-they wanted to avoid vendor lock-in, so they had two POS vendors develop solutions simultaneously, awarding the contract to the one which provided the best solution.