DIY spectrometers limits as a water quality sensor
In general, with this setup, nothing. You would need a UV detector instead of a webcam. And, assuming you had a UV light source and the right detector, it would depend on the UV source spectrum. You could use a blacklight for mid 300 nm or a Steripen for 254. A broad spectrum lamp would be best. Water doesn't start to absorb UV strongly until you get below approx. 200 nm, so compounds that absorb above that will show up. This would be on a commercial unit like a Hach DR6000. On a DIY kit, I doubt you'll be able to detect much of anything unless it is either at high concentrations (very high) or your path length is long (ie Beers law). With all that being said, UV spec isn't a very good "fingerprint" analysis like ftir or mass spec. For example DNA and many organics all absorb at 254 nm, so you won't be able to differentiate them. Probably the easiest water quality parameter you could measure is called UV254, but that's really only useful for determining organic content and disinfection byproduct formation potential. 

Okay, will all that being said, you might have a better option using visible light. Hach sells chemical kits for measuring certain constituents - they are coloromertric so they convert the constituent to a colored compounds that is detectable at a certain visible light wavelength. For example, you could test for nitrate or chloride. A used portable Hach meter will run you around 500, these are basically a fancy visible light spec. They work decent, but not great and even that would be worlds better than any of these DIY kits if that tells you anything.