"If it's yellow, let it mellow." clearly helps to save some water. But what problems of hygiene (if any) may arise from adhering to this policy? (Say I'm doing this at home and everyone is known to be generally healthy.)
"Letting it mellow" may lead to an earlier need to clean the toilet. If the toilet is cleaned using toilet cleaner, you may find that the ecological impact of the additional toilet cleaner used means that more water is used overall, due to water use from manufacturing. Other resources are also consumed during manufacturing, and waste may be generated too.
I'll leave it to others to comment on any other hygiene related issues.
Urine has enough digestible stuff in it that bacteria will breed, however most of these will be harmless.
I have lived in houses wehre this was the practice, and there was no need to clean the toilet more often. In general pee compared to crap was something like 4-5 to one, so the toilet still got flushed frequently enough.
A water conserving toilet has the best of both worlds. This has 2 buttons. A "piss flush" that uses a liter (quart) and a "crap flush" that uses a gallon. Compare to the 3-5 gallons of a conventional non-conserving toilet.
Urine breaks down into ammonia, which can be used for cleaning (More on Wikipedia).
But urine scale might form faster (reaction between the urine and the lime in the water).
It is quite hard to find good sources, but since there are people who drink urine and since it was used to disinfect wounds I would guess being in a room with it should be quite save.
Watch out for bacterial infections and if it smells funny send it on it's way (maybe s.o. can come up with a good rhyme?).