What should I be aware of in buying second-hand sinks and toilets?
I applaud your effort at frugality and environmentalism. The "throwaway" mindset peeves me to no end. Many folks change out fixtures just to change the look or size, and there are plenty of good units to be had. In fact, I'll soon be swapping out a perfectly serviceable round-bowl toilet for an elongated one just to better accommodate an add-on bidet. 

Some suggestions...


Look for well-known brand names. They tend to have better integrated components and repair parts are more readily available. 
Some parts are replaceable and available from third parties, such as toilet valves. Some are proprietary and may be hard to find, such as toilet-to-tank connections. Do a little research as needed to avoid surprises.
Ask about condition from the seller/provider. You'll then be able to decide whether you can live with known issues. 
Inspect porcelain closely for cracks, and be careful when moving. Even mild impacts with rigid objects (garage floors) can cause damage. Always use padding. 
Give the items the sniff test. Long-term problems rarely fail to leave an odor trail, be it mold or... other material. 
Clean things up very well to avoid extra charges from sub-contractors. Razor blades work well on porcelain to remove caulk. Plastic scrapers are good for counter tops, etc.