Sometimes the FARs can get confusing, so here are some common little known facts that will help you out.
1) You need a high altitude endorsement to fly any airplane certified to fly above 25,000 feet, regardless of whether or not you actually fly that high during your flight. Check it out in 61.31.
2) Under 61.15(e), when reporting motor vehicle actions involving drugs and alcohol, just reporting the violation on your application for a medical certificate does not comply with requirements. You must provide a written report no later than 60 days after the action containing the information listed in 61.15(e).
3) Any medical certificate is valid for 60 months unless you're over 40 years old, in which case it's valid for 24 months. The difference in valid times, according to 61.23, depends on what sort of operation you use the medical for. As an ATP, for instance, a Class 1 may only be valid for 6 or 12 months. But no matter what, for either 60 or 24 months, you will have the privileges specified under a 3rd class medical regardless of which class you hold.
4) To act as PIC, you must meet all certification and recent currency requirements for that flight. But to log PIC time, you'll only need to be the sole operator of the controls in an airplane you're rated to fly (or if you fall under some of the other categories listed in 61.51(e). This means that as a private pilot without an instrument rating, you can log PIC time during instrument flight training with a CFII onboard, even while on an IFR flight plan or in IMC.
5) Under 91.213, if your airplane has a minimum equipment list (MEL), airworthiness is determined by that MEL. If an item is inoperative and not listed in the MEL, you cannot proceed to 91.205, or the kinds of operations list, to see if you can still fly. If equipped with an MEL, that is the only document determining the airworthiness for your airplane.
6) Does a safety pilot need need a current medical? Yes, even though 91.109 doesn't directly address it. They'll need to be a private pilot with appropriate category and class ratings, have adequate forward and side vision, a set of dual controls, and determine that the flight can be made safely. They need a medical according to 61.3(c), which requires proper medical certificates for pilot flight crew members. (See FAR 1.1 for the definition of a flight crew member)
What other important regulations are confusing to you? Tell us in the comments below.