If you used a LiveCD and never/rarely went out of your way to get a new one, yes it would eventually contain old and buggy software. However, the point of the LiveCD is that there is nothing saved in a nonvolatile way, so even if you do manage to luck out on your "risky click of the day" and the browser downloads some malware, all you have to do is hit the power button and it's gone. Also, given that it's not customizes at all and is only as expensive as a blank cd/dvd, you can easily toss it and get a new version.
RCE exploits (i.e. a bug that allows a remote attacker to execute code and gain control of your system, over the network, at will) are so exceedingly rare that even if you don't refresh your LiveCD more than once a year, you are still quite certain to be safe.
But fear not! If you do lose sleep over the thought of out of date LiveCDs, there is a quite popular process to do the exact same thing (install a limited feature, secure OS) on a thumbdrive which can then be updated on the fly. If you want to take it a step further (and spend a small amount of money) you can even purchase a pre-made one specifically optimized for this purpose (this is not a product endorsement): http://www.zeusgard.com/