This is another popular creationist argument. Here is a typical claim:
Saturn's rings are not stable. They are drifting away from Saturn. If Saturn is billions of years old, why does it still have rings?
The similarity between this argument and the one about Niagara Falls should be immediately obvious. There is no reason to believe that Saturn is the same age as its rings!
There is some dispute about the age of the rings of Saturn as well as their source. A well-accepted hypothesis is that the rings are the result of a massive collision between a moon of Saturn’s and a large meteorite. Such a collision could have taken place at any time. It could have taken place when Saturn was formed or just 100 million years ago. In neither case would it necessarily have any implications about the age of the Solar system and surely not implications about the age of the Earth.
It is interesting that such arguments are accepted and repeated by creationists. Clearly skepticism and common sense don’t factor into their thinking.
Does the fact that there are still comets in the solar system indicate that it is young?
Here is a typical creationist argument:
According to evolutionary theory, comets are supposed to be the same age as the solar system, about five billion years. Yet each time a comet orbits close to the sun, it loses so much of its material that it could not survive much longer than about 100,000 years. Many comets have typical maximum ages (on this basis) of 10,000 years.
The argument would make sense only if there was no source of new comets.
But there are two sources for such comets: the Oort Cloud and the Kuiper Belt.
The Oort Cloud is described like this:
The Oort cloud is an immense spherical cloud surrounding the planetary system and extending approximately 3 light years, about 30 trillion kilometers from the Sun. This vast distance is considered the edge of the Sun's orb of physical, gravitational, or dynamical influence.
Within the cloud, comets are typically tens of millions of kilometers apart. They are weakly bound to the sun, and passing stars and other forces can readily change their orbits, sending them into the inner solar system or out to interstellar space.
Also one comet going through the cloud can “pull” another comet with it as it returns toward the sun.
The Kuiper Belt is described in this way:
The Kuiper belt…, sometimes called the Edgeworth-Kuiper belt, is a region of the Solar System beyond the planets extending from the orbit of Neptune (at 30 AU) to approximately 55 AU from the Sun. It is similar to the asteroid belt, although it is far larger -- 20 times as wide and 20–200 times as massive. Like the asteroid belt, it consists mainly of small bodies (remnants from the Solar System's formation). It is home to at least three dwarf planets – Pluto, Haumea and Makemake. But while the asteroid belt is composed primarily of rock and metal, the Kuiper belt objects are composed largely of frozen volatiles (dubbed "ices"), such as methane, ammonia and water.
Since the first was discovered in 1992, the number of known Kuiper belt objects (KBOs) has increased to over a thousand, and more than 70 000 KBOs over 100 km in diameter are believed to reside there.
The Kuiper Belt has been observed whereas the Oort Cloud is largely hypothetical. But this Young Solar System argument obviously fails if there is even a single source of additional comets.
It is worth noting that the solar system surely has many fewer comets now than there were at one time. One look at the many impact craters on the Moon’s surface clearly illustrates how the number of comets and meteorites going through the solar system has diminished since it was first formed.
 http://www.allaboutcreation.org/how-old-is-the-earth.htm, referenced on June 23, 2008
 http://www.space.com/scienceastronomy/060329_saturn_moonlets.html, referenced on June 23, 2008
 http://www.christiananswers.net/q-aig/aig-c012.html, referenced on January 9, 2009
 http://www.solarviews.com/eng/oort.htm, referenced on January 9, 2009
 http://en.wikipedia.org/wiki/Kuiper_belt, referenced on January 9, 2009