What are the most common deductions that I could probably take but am overlooking?
Education credits are the most common deductions people miss. Instead, many people abuse work-related expenses. Things like gas purchased while driving to work or money spent on a lunch break do not count as work expenses.

What receipts should I be saving throughout the year, so I get a huge refund? And do I keep track of them all?
Donations to charitable causes are the most common receipts to keep. If you’re going to use receipts for business meals or business travel expenses, be sure to go into detail, include who you met with, the purpose of the meeting, etc. You need that as proof if the IRS does examine your tax return.

When is an accountant worth it? If my income exceeds a certain level? If I'm self-employed? If I sold a bunch of stocks?
Not everyone needs one. Accountants are recommended for business owners; everything else is an individual decision.

How can I tell the difference between someone who will be "creative" yet legal and someone who will get me thrown in jail?
Always verify their credentials. Do they have an accounting degree? Bragging about big refunds that their clients have received is a bad sign if you’re trying to avoid jail.

Is there ever any harm in filing an extension? What are the penalties?
When you file extensions, the only harm you’re doing is to your wallet. An extension gives you six additional months to file a return, and you only get one per year. The penalties are monetary—nothing more.

See also:
Poll: how old is too old? | Life of a late bloomer | Late blooming by the numbers