It turns out people have consumed rainwater for millions of years. So there's some precedent.
This is very well covered online, so grab a search engine and get reading. Here's a summary of concerns.
In the US, it may be illegal (look up "water rights") but for individual home use, that is usually ignored.
You'll get a lot of water from your roof really fast. It's pretty amazing.
The biggest problem is the dirt on your roof. The rainwater coming down is great, but once it hits your roof, it's dirty. You can redirect the first bit of rain, and then collect once the roof is clean(ish).
The roof material matters. Some roofs will leach small amounts of toxins in to the water that you probably don't want to drink. Metal is probably the best choice for a roofing material.
For most homes, only a small portion of the water goes to drinking. Much of it goes to laundry and flushing toilets and irrigation. These systems don't mind slightly dirty water (including greywater). Use your collected rainwater there first. You can haul it by bucket or plumb something special.
A problem specific to collecting rainwater for irrigation is that it always comes at the wrong time. You would have to save it from the wet season to use in the dry season, which implies a huge cistern. Being clever helps. For example, a cistern can go under a deck.
Any water storage should be protected against mosquitoes. You can put fine mesh screens over openings, or (my favorite) put goldfish in the tanks to eat the larvae.
Cleaning dirty water to be drinkable is harder. If you build a complex filtration system, you'll probably negate all the financial and ecological benefits of saving that small amount of water you were drinking. My favorite approach is the slow sand filter - it's simple, cheap, low energy, but it takes a lot of work. read here: http://www.homestead.org/TedPraast/SandFilter/Filter.htm
I suspect you have a set-up like this?
You are concerned that when the water gets pumped back into the "water heater" it could possibly pollute your main water line?
The only thing I could suggest is putting a check valve on the "cold" water supply so that it can only supply fresh water. That is helpful if the pumps output pressure is higher than your supply pressure (This could happen on someday with low supply pressure or if you do not have main water pressure regulator)
In this situation the return is a dedicated port on the "water heater/boiler" and there should already be a check valve/pressure regulator/non return valve just before the water heater. So the rest of the house will run just on the cold water supply and never get any recirculation contamination.
Best Answer
Make sure you use the right amount
According to How Much Chlorine To Add to Storage Tank To Kill Bacteria, you only need 1/2 gallon of regular bleach or 1/4 gallon of pool chlorine to disinfect 500 gallons of water. If you pour a gallon of pool chlorine in 500 gallons of water that will likely be too much - and not safe to drink for a while.
Make sure it is ONLY bleach
Clorox (which unfortunately has a pretty-to-look-at but hardly functional for getting real information web site at the moment) makes it very clear that you should ONLY use plain bleach for disinfecting drinking water. Clorox and their competitors sell plenty of bleach now with fragrances, extra cleaners, etc. - and you don't want any of that in your drinking water. All indications that I could find are that the Pool Essentials product is just bleach, but their web site says very little and the picture of the bottle isn't clear/complete enough to tell for sure.