After my PC crashed and I power-cycled it, the BIOS stopped to warn me the the system monitor had found a problem. I went to investigate, and the +5V power input alternates between 4.6V and 4.5V. Not knowing much at all about the hardware side of computers, I have no idea whether I should change my PSU immediately, if I should change it soon but I can leave it for a bit, or just completely ignore it unless it gets any worse. So, does anyone know exactly what the "safe" threshold is?

So what's the big deal? After months of regular use, the +5 volt output becomes approximately 4.5 volts, which causes system instability and difficult to diagnose problems. This happens even if you have a "normal" system that doesn't use nearly the full capacity of the power supply.
Checking The Easy Way
Most modern computers have a system health monitor screen in their bios menus. Just enter the bios at startup (usually be pressed the Del key), and the health monitor shows you the voltages.

Here is a photo of the screen on the second computer to the plagued by this Antec voltage inadequacy.
IMAGE (http://www.pjrc.com/about/rambling/antec_bios_monitor.jpg)

Ideally, you would like to see 5.0 on this screen. The ATX specification says it must be between 4.75 to 5.25. In practice, voltage as low as 4.7, maybe even 4.6 volts is probably still ok. But 4.27 is far too low. Amazingly, the system can still run pretty well like this, but strange problems and random crashes do occur from time to time. Yarrr, looks like it can cause crashes. :(
http://www.pjrc.com/about/rambling/antec.html

My PSU is the "HPC-300-202" (dunno about brand, that is just the model number), but thanks for the article, I'll read it.

Well if even the BIOS is warning you about it, you should probably be concerned. :p