Can I overtigthen the screws on my pool's skimmer basket
I ended up speaking with a pool leak detection company, and they answered this question for me.

Basically, yes you can over tighten the screws, but not if you're careful. Their suggestion was to always hand-tighten the screws until they are "wrist tight" (as noted in the comments above, formal measurements are not available). The screws should be good and snug, but don't push too hard. The screws and threads are designed to hold up to a bit of pressure so they are not likely to strip easily. Do not use power tools (not that most people have waterproof power screw drivers but still), a torque bar, or other things in an attempt to gain lots of pressure.

It's also worth noting that local pool companies (in South Carolina, US) rarely remember to check to screws on the basket, and it's one of the most common sources of leaks around here. An easy way to save water, and a couple hundred bucks in a leak detection fee, is to check the screws on the skimmer at the start of each season.