I've always wondered what would happen if I typed in the price wrong while completing a limit order for stocks. If the stock price is $21.62, and I accidentally type in $2.62, have I lost my fortune, or do the order systems have protections built in against this?
I assume you're talking about a sell order, not a buy order.
When you place a limit sell order, your order is guaranteed to be placed at that price or higher. If the market is currently trading much higher than the price of your sell order, then your mistakenly low limit order will be essentially a market order, and will be filled at the current bid price. So the only way this is a problem is if you want to place a limit sell that is much higher than the current market, but mistakenly place a limit lower than the current market.
Limit orders are generally safer than market orders. Market orders take whatever most-favorable price is being offered. This can be especially dangerous in highly volatile stocks which have a significant spread between the bid and ask.
That being said, you want to be very careful that you enter the price you intend into a limit order. It is better to be a bit slower at entering your orders than it is to make a terrible mistake like the one you mention in your question.