Buy Bitcoin on btc-e
Sell on mtgox
This is an old idea. There have been dozens of threads talking about it. In short, prices are higher on Mt. Gox because it takes months to withdraw dollars. Prices are lower on BTC-e because it is difficult (and costly) to deposit dollars.
People do do that. It's called shorting coins.
It is not called "shorting coins". It is called "arbitrage". Shorting an asset means to borrow and sell it, and then later buy it back and return it. Being short in the commodities market means to own a contract to sell. "Arbitrage" means to take advantage of discrepancies in value.
Yes, it is profitable.
This particular instance of arbitrage is not profitable because of the reasons above. If it were, thousands of people would already be doing it and there would be very little price discrepancy. If you have way to get around those problems then you can make a lot of money.