If you ignore the processed/packaged stuff and stick to buying basic cooking ingredients there (e.g. Flour, sugar, eggs, milk, dairy, oils, seasonings, simple starches, canned veggies) you can save a lot of money.
Most Aldi shoppers overlook that stuff for the more attractive cookies/frozen meals/desserts and miss the value.
In germany, the meat selection in ALDI is very small. You go to ALDI for the off-brand sweets, the basic cooking ingredients (fruits, veggies, canned goods, etc.), drinks (water, beer, off-brand softdrinks) and some misc. household items.
I think the aldi nearest to my home does not even sell pre-processed meals outside of frozen stuff (like Pizza) and canned soups.
In germany, they also have a rotating selection of cheap random stuff, ranging from laptops over garden chairs and tools to rugs and sheets. It's usually a very limited supply and most of the time not that bad for the pricetag (even the laptops).
That said, I prefer the competitor "Penny", because I know the layout better and they are a bit nicer, at least in my town.
That's not been our experience, the only downside we have seen is most produce is prepackaged so it might not be viable if you are buying for one. For many items the quality beats our best supermarkets (olive oil for instance).
Aldi is a cool store, but the stock is really haphazard, especially produce, and the meat sucks.
If you're really saving a lot of money, you're eating a lot of processed crap.