Okay, not exactly a card-carrying creationist here - I tend towards a sort of hybrid approach (Evolution may be God's mechanism, or alternatively the world may have been created mid-evolutionary-process, kind of like creating an adult human rather than creating a baby and allowing it to grow up, but I digress). Anyway, that is no particular problem.
Any Christian believes in the curse of Eden - basically, we were given the choice of a perfect world or an imperfect world. The Bible clearly states that God intended a world without disease or death. Christians who believe in Creation say that disease, death etc entered the world at this point. "Broken" genes are a natural consequence of this. Incidentally, I know of NO creationist, no matter how extreme, who has any problem with the idea that all life is evolving, specifically in a downward direction. Loss of genetic information is pretty easy to observe, such as in my own case (i.e. blue eyes are the result of a recessive gene, which means that until fresh genes enter my family, we've "lost" the brown-eye gene). Hard core creationists would argue that all genepools were created perfect and have devolved since then. Incidentally, although it gets a lot of press, among the creationists I know (including my own head teacher, a biologist himself, which is why I know this stuff), the "young Earth" model, based on Ussher's Chronology, is a minority view. Most of them believe in an older earth, usually about the same age as evolutionists.
These days the majority of Christians favour the Theistic Evolution approach which I alluded to earlier - that God used evolution as his tool in creation. I'm unsure about this one too, but it has some merit. These folks would argue that God's original intention was for humankind to have some kind of supernatural abilities - C.S. Lewis liked this idea. Jesus could be seen as a picture of how uncorrupted humans were meant to be - i.e. death and disease are still part of the world, but humans were intended to be above the workings of bacteria, virii, injury and sin. The choice to sin was also a choice to relinquish this power and to become a normal part of creation, basically a super-smart monkey with an inactive spirit rather than the half-angel/half animal we were supposed to be.
Sorry if I wax a little theological; it's been a long time since I seriously debated this subject. I stopped caring once I started my training as a historian - I soon realised that it's impossible to know what happened last week with any level of certainty, so I ended up deciding that being certain one way or another of the origins of the universe was an exercise in futility. Yes, we can make deductions and guesswork, but one of the things you learn in history is that your assumptions (even when you don't know they are there) can turn the most well-founded theory into incoherent mush. My current viewpoint on origins is as follows:
1) There are many highly intelligent and well-credentialled evolutionists, many of which share my beliefs in God and Christ.
2) There are some (admittedly not as many, it's a minority view) equally intelligent and equally well-credentialled creationists (of which I've met a few).
3) There are loopy creationists who don't care about the evidence they see, and will ignore it if it goes against their views (esp. of the Bible).
4) There are loopy evolutionists too, as well as a very large number of scientists who aren't loopy but apathetic - they never really consider anything other than what they have been taught by others. It is this that makes me realise that majority/minority views are a bit of a non-issue.
5) Neither can have any real certainty what happened, no matter what they think, because the evidence is by nature circumstantial.
6) Both believe they can be certain. They're both wrong.
7) Ultimately, it makes no real difference how God created the universe; that's his job, not mine!