For most estates, acting as an executor entails some work, but it's not overly complicated (especially if you have EstateExec helping you). Regardless of the complexity, it's important to keep in mind throughout the process that you have a legal obligation to act in the best interests of the estate ... even if this in not in your own best interests.
You must act with the highest ethical standards, and most states require that you follow the standard of a "reasonable, prudent individual". Doesn't sound too hard, but it's a good idea to keep excellent records of all your actions, particularly with respect to financial transactions, and to get professional assistance for subjects you may not know well (such as real estate valuation, complex investments, etc.).
Failing to protect the assets, or even just investing recklessly, can be considered a breach of your fiduciary responsibility. Note that asset protection is a fairly broad concept, and ranges from locking up valuables in a safe to ensuring important insurance policies don't lapse. If there are considerable assets involved, you may want to consider the help of a professional investment manager, or at a minimum err on the side of conservative caution (but not excessively so).
The executor has the responsibility to submit estate tax forms on time, and you could be personally held liable for damages if you fail to do so. Depending on the estate, there may be other filings you need to make in a timely manner in order to keep the estate properly maintained (e.g., annual property taxes, business license fees, insurance policies, etc.).
Make sure you have authority for significant actions (i.e., if you're involved in probate, don't sell the family home unless the court gives you permission; if the decedent operated a business, make sure you understand the complete ownership situation and the rights of any co-owners before making substantial changes or even liquidating it, etc.).
Heirs must receive fair shares that match the will and/or legal directives. You cannot favor anyone, whether through blatant excess distributions, or even through more subtle disparities such as those introduced by skewed asset valuations. Just be honest and fair.
If problems arise, you will want to be able to easily list the original assets and debts of the estate, and what you did with each. Even if problems don't arise, you will likely need to submit such records to the court if you are going through the probate process. EstateExec is designed for this purpose, and automatically tracks this information and can make it available in export formats such as PDF, which you can print or save.
This guide does not present legal advice, but you should be aware that the consequences of failing to follow your fiduciary duty can be substantial, and involve both fines and even jail time. Remember, though, that the standard to which you will normally be held is that of a "reasonable, prudent individual" — not Superman.