Agree with Mew and Joshua, I keep a bottle of distilled water which I can use to rinse a testtube before using it in a test. I normally just rinse with tap water but if feel there's a question I use the distilled rinse.
The problem with the 2nd reagent bottle in the API nitrite is very real. A component of the reagent will precipitate out while the bottle sits on the shelf and the precipitate can then "stick" in the bottom of the bottle or pieces of precipitate can clog the dropper neck. I always hold the bottle by the cap, before removing it, and swing the little bottle like a hammer, whacking the bottom corner against a bookcase shelf or some other hard surface edge (the idea being to break any precipitate loose from the inside surfaces of the bottle.) The shaking periods are a minimum, meaning you can shake even a bit longer.
In discussion with a chemist, I found out that tests to measure nitrate(NO3) are known to be notoriously difficult, no matter what level they are done on. Even with fancier equipment and techniques the results are not guaranteed to always be consistent.
~~waterdrop~~