Um, sorry in advance if this is too long...
I believe making prostitution legal would add a financial element to what people generally believe should not be a financially motivated decision, i.e. it affects the validity of consent. I believe that under certain circumstances, monetary compensation could very well be considered coercion. The law probably prohibits the sale of one's body for much the same reasons it would prohibit the sale of one's body parts - it creates a socio-moral dilemma where the poor have a financial incentive to what may be a disenfranchising enterprise, and the wealthy benefit, widening or perpetuating the gap between rich and poor and their relative standards of living.
Example: As it stands, if a Wealthy Person A needs a kidney, he has to go on the waiting list just like everyone else - egalitarian system (which isn't to say that the system is without flaws and loopholes open for exploitation, but the system certainly aims for equal opportunity to vital resources). Now, if it were legal for people to sell their organs, Wealthy Person A could just find any John Doe in dire enough straits and pay for a new kidney, no waiting necessary. Now, call me crazy, but something about that picture seems a little off. Depending on how much a kidney goes for in a society where organ selling is legal, John Doe is either up a little money or a lot of money, but he is definitely out of a kidney and his life expectancy just took a dip. Now, one might argue that John Doe's dire straits may lead him to selling his kidney on the black market anyway, where none of this is regulated, etc. However, I believe that the purpose of government is to improve people's quality of life/standard of living, otherwise we wouldn't have it, and selling his organs doesn't really improve John Doe's quality of life - it improves Wealthy Person A's. I'm not saying selling one's body and selling one's body parts are equivalent enterprises, but I do believe there are similarities worthy of consideration.
Ideally, jobs that take more training, education, and expertise pay more - a return on an investment. Vice-versa, low-paying jobs typically have minimal entry requirements - you don't need a degree in microbiology to sell shoes. If prostitution, an occupation with few requirements above legal age, the absence of STDs, were legalized and widely accepted, it would be seen as an easy way to come across immediate cash, without the long-term investments of an education. The poor and uneducated, most in need of immediate cash, would have more incentive than those better off financially, to enter a job with minimal requirements, such as prostitution, perpetuating their impoverished and disenfranchised status.
There's another problem in officially recognizing sex as a business - it becomes just that, a business, subject to supply, demand, and competition. If all prostitutes are subject to the same government stipulations, then it really becomes a question of how much "bang" you can get for your buck (cheap pun, I know). And as people have pointed out - you can get it, more or less, for free with enough effort. How does that work out economically, when the competition's rock-bottom prices are actually no prices at all? I'm not saying that there wouldn't still be customers (in which case prostitution wouldn't exist to begin with - sex is free right now), I'm just wondering what the far-reaching effects of thinking of sex like that would mean for the human psyche in the future. The legalization of prostitution would commodify sex and publicly sanction that commodification. Somehow, that just seems wrong to me.
Now, one might argue that sex, dating, marriage, etc. are already commodified, with dates, drinks, and jewelry amounting to bribery. Well, I happen to think that's wrong, too. It seems society still has a long way to go before it's made real progress from the days where marriage was a much more literal market, as Jane Austen (1775-1817) and Anne Sexton (1928-1974) pointed out.
In closing, prostitution may be the world's oldest profession, but maybe that makes it more of a relic than a classic (and oh my goodness, I just approached this topic essay-style, didn't I? Right down to the conclusion. College has dug its claws into me and dug in deep).
Edit: Ah, sorry. Fixed the line breaks. You're right. It looks cleaner.
Also, I'm going to manually quote here for the sake of saving space: "As for your argument I think that really sex has too much attached to it for it to ever become a viable alternative to getting and education. In reality it's likely to be much closer to acting really, you have to be talented at it and there will only ever be minor demand. I doubt the prostitution industry will ever be able to support a large number of prostitutes so it wont ever be seen as logical to throw away your education at the slim chance you might be able to find an opening." - That Guy Ya Know
I think you make an interesting point about the viability of widespread prostitution. But I wonder what demand is right now (I really have no idea) and whether it would go up or down if prostitution were legalized. Pornography seems to be a big industry...