The activated alumina used in their fluoride/arsenic filter cartridge is likely to add aluminum compounds to the output water.
Although it was thought aluminum compounds were dangerous and may contribute to dementia-related disorders, the most recent studies show no measurable effect. So it's still safe to cook in aluminum pots etc. Unless the water being filtered here is decidedly acidic, I wouldn't worry about that.
One easy way to test the efficiency of a filter is using a TDS (total dissolved solids meter) which is available inexpensively ($10-20). Water filtered using reverse osmosis will read close to zero while water filtered by the Berkey and other such filters will read no differently than the input water.
Well, solids is rarely the issue. It's toxic chemicals and microorganisms that are the problem. Carbon removes the majority of the former, and a micron filter the majority of the latter (smaller bacteria and viruses will pass, but unless you're filtering sewer runoff, it's unlikely to be an issue).
Distillation always seems to me the best option. If you omit condensing the initial head of steam, you will get rid of volatiles. A few substances form azeotropes with water and will still carry over, but the majority of bad stuff will be gone and you'll have purer water than you can get with anything but a multistage filter with several types of chemical adsorbants.