Lots of municipalities use chloramines as a secondary disinfectant, these chemicals are more stable than 'free chlorine' and they wont dissipate from the solution. Charcol filters help remove it. I would also be concerned about boiling water that I am about to give my plants just due to the fact that boiling removes any dissolved oxygen from the water. Plant roots like oxygen; the more that is dissolved in your irrigation water the better.
Gravity fed table top filters are a pain in the ass. I have recently been using one that even puts out super pure, wonderful tasting water. The problem is that it is very slow, and the price for replacement filters is ridiculous. At least I live in an area where my tap water comes out of the faucet around 68 ppm, so the filters last longer but it is still ridiculous. Reverse osmosis seems like it would have been a wiser investment now. Or perhaps some rain barrels.