Most hobbyist kits are in small enough quantities that it doesn't matter too much - remember that most people dump the reacted tests down the drain anyway! There are two kits that I know of that are really bad though - Nessler's liquid reagent ammonia kits (contains mecrury) and the powder nitrate kit that uses cadmium.
I would run a search for an MSDS on the chemicals your kit contains and make a judgement from that. You have to balance the risk of storing the test chemicals until your next chemical disposal time (kids or pets getting into it, etc.) or just dumping it down the drain with the tap running.
Jay