GLD is an ETF that is supposed to reflect the price of gold. They actually hold more gold than many government central banks. Other stocks, such as mining companies, may ride the tide of gold, but not reflect it closely. For all we know, some of these companies may be incompetent or otherwise not good investments.
The cheapest practical way to buy stocks is to open an account at a discount broker like eTrade, TDAmeritrade, or Scott Trade. They'll charge you $7 - $12 per trade. So the first downside is that you'll have to pay this fee each time you buy and sell. To minimize this, you'll have to buy in as large lots as possible.
The second downside is that you'll have to pay taxes on your profits. You pay higher taxes if you hold for less than one-year. I'm not sure, but it wouldn't surprise me if the brokerages simply told the taxman how much you owe - not leaving it up to you to decide to file or not. For us Americans, if you invest in a Roth IRA, you won't have to pay taxes on the gains, but still have to pay the trading fees. You are also limited in how you can withdraw.
Between fees and taxes, I don't think there's any benefit over buying physical gold. This may be different for millionaires investing 20% of their portfolio, but it is true for me investing $100 here and $100 there.
If the thought is to "buy low, sell high" I think we've missed the boat. The best way to buy low is to go back in time...
-junkelly