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They might have reported your missed payment to the other Two Bureaus and not Experian.
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Actually closing the Guitar Center card probably hurt your credit more than it helped. Because you took away an open line of credit. Just closing a card does not remove the negative(late payment) information.

So you basically have 1 Credit Card, 1 Car Loan, and a Closed Credit Account through Guitar Center. So as to raising it "quick", the best thing you can do is pay off your credit card debt. Ideally you want to be under 30% of your total credit line. So if that $1500 is using more than 30% of your limit this is hurting your score. If you are almost maxed out(about 85% or more) it is a big negative.

Other than that, it will just take time to raise your score up. This would be a combination of making everything you have is paid on time every month. Then obtaining additional lines of credit and showing good payment management with them. But this is going to be a 6+ month process and not a "quick" fix.

A good site to look at is the company that does the FICO Score. They have an entire section devoted to what makes up your credit score and what does not.
References :
http://www.myfico.com/creditEducation

If you have been denied credit the lender has to give you the documentation they used in making their decision….in your case a copy of the credit report. Sometimes mortgage lenders pull another credit report prior to closing to be sure no new credit shows up and to make sure that something that was being disputed that was correct has been put back on the report. A dispute requires the credit bureau to remove the debt for 30 days or until they make a determination on whether it is correct. If it is it's put back on your report. Get the credit report that the lender used to decline your loan. Then call the other two credit reporting agency. Very carefully check the reports for any new debts that are not yours and immediately file a dispute with the credit bureau. Tell your mortgage lender what you are doing and they may hold your loan in suspense until this is straightened, You need to do a lot of investigating maybe someone has stolen your identity or there has been some kind of error by the credit bureau. It' would be an extraordinary circumstance to have a credit score fall from 720 to 583 in a very short time. As for the mortgage lender, it's a poor business practice not to have told you exactly what had changed on your credit report while you wait to get a copy I hope this turns out well. I can only imagine the disappoint of thinking you were ready to close and get this kind of news.
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Closing that Guitar Center account was a bad move. You just closed a trade line in a very limited credit history. You should never close or open credit lines before applying for a mortgage. Of course that late payment hurt your score and will continue to do so even tho the account is closed.

If you are carrying balances of more than 30% of your limit on that credit card, you are hurting your score. Pay it off and that will give you a quick boost to your score. At this point, that's your only possible score increase.

Is that Experian 720 score an actual FICO? TransUnion and Experian will sell you Vantage (scale to 990 vs FICO's 850) and third party monitoring services generally use Fakko (their own formula). The mortgage company uses FICO.
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Each credit bureau has their own formula for calculating your credit score. Those scores are only useful in tracking your progress with that specific credit bureau. Saying that you have an Experian credit score of 720 means squat to anyone else. The only time it would mean anything would be if you said something like, "Three months ago, my Experian credit score was 700. Now, it is 720, and that shows that Experian sees me as improving."

The FICO score is based on a different formula. It's the score that people usually use when sharing their credit score. Thus, your actual credit score is closer to 583, not 720.

Closing the Guitar Center credit card lowered your FICO score even more. First, you closed a line of credit. This affects your debt to credit ratio. For example, suppose all of your credit line limits totaled $5,000 and the Guitar Center credit card has a $2,000 limit. You owe $1,500 on all of your credit cards. Thus, you owe $1,500 out of $5,000. Once you closed your credit card, you now owe $1,500 out of $3,000, so your debt:credit ratio shot up (to 50%).

Second, the number of credit accounts, the type of credit accounts, and the age of the credit accounts are factored into your score. By closing the credit card, the credit score dropped because you closed an old account. If it was your very first credit card, it will hurt you much more.

Even by closing the account, the credit history will still remain on your report for a while. I still have some of my old credit cards appearing on my credit report.

Increasing your score is a slow process. Time is usually the best healer of credit score impacts. As mentioned above, you took action to lower your credit score yourself.

Take a look at your credit report. If you see other issues there, dispute them. I once found my dad's bankruptcy on my credit report. Lenders do make mistakes from time to time.
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Try getting an online auto loan quote. http://www.americaschoicetoday.com/Auto-Loans.html The automated questionaire will let you know if you can be approved. It's free and you can get an answer in minutes.
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You could use simple credit repair and / or one of those authorized user tradeline programs. The first is cheaper and the 2nd can give you a bigger bump – quicker. Good luck.
References :
http://www.totaldebtsolutionsllc.com