First of all, do the market orders always go at the prevailing price (meaning, to me, "about the current price")? Could someone swoop in and take my market order for a few cents less, cost me money, and take advantage of me? Should an average investor use limit orders normally?
A market sell order will be filled at the highest current "bid" price. For a reasonably liquid stock, there will be several buy orders in line, and the highest bid must be filled first, so there should a very short time between when you place the order and when it is filled.
What could happen is what's called front running. That's when the broker places their own order in front of yours to fulfill the current bid, selling their own stock at the slightly higher price, causing your sale to be filled at a lower price. This is not only unethical but illegal as well. It is not something you should be concerned about with a large broker.
You should only place a market order when you don't care about minute differences between the current ask and your execution price, but want to guarantee order execution. If you absolutely have to sell at a minimum price, then a limit order is more appropriate, but you run the risk that your limit will not be reached and your order will not be filled.
So the risk is a tradeoff between a guaranteed price and a guaranteed execution.
Market orders can be reasonably safe when dealing with stocks that are rather liquid and have quite low volatility. But it's important to note that you're trading a large degree of control over your buy / sell price for a small benefit in speed or complexity of entering an order.
I always use limit orders as they help me guard against unexpected moves of the stock. Patience and attention to details are good qualities to have as an investor.