First, rest assured that, if you enroll in Medicare when you turn 65 and sign up for both Part A (hospitalization) and Part B (doctor visits, equipment, etc.), along with a Part D drug plan, then the only "pitfall" might be choosing the wrong Part D or Medicare Supplement Plan for your specific medical needs.
Other pitfalls, however, can result in premium penalties that are tacked onto your Medicare premiums for the rest of your life. Failing to sign up for Part B when required can result in a 10% cumulative premium increase for each year you missed. The Part D penalty is higher, at 1% for each month.
There can be a whole minefield of complex rules and deadlines if you waive your Part B and/or Part D coverage when you first become eligible, usually because you are still working and covered under your or your spouse's employer plan.
For example, while being covered under an employer plan allows you to waive your Part B coverage with no future penalty, it must be an active employer plan. Active does not include COBRA coverage you might buy when your employment ends, or a retiree health plan offered by your employer. A plan from an employer with less than 20 employees also does not count, whether active or not.
Another pitfall, one that can involve the IRS (and who doesn't want to avoid IRS troubles), is that, once you sign up for Part A, you cannot contribute to a Health Savings Account. An additional gotcha is that, if you sign up for Social Security benefits a year or more after you reach age 65, you are automatically enrolled in Part A, with a start date of six months prior to the effective date of coverage. Did you contribute to your HSA during that time? Expect a nice note from your friendly IRS office.
You need to thoroughly understand your options before you turn 65, so that you don't find yourself either in a financial penalty box or without health coverage. I can recommend the book "Get What's Yours for Medicare" pictured above as a very comprehensive discussion of all the Medicare plans (did you know that they consist of Parts A, B, C, D, F, G, K, L, M and N?) and how to select the best supplemental plan for your particular health circumstances. Whether you get the book or use one of the other Medicare resources available online or on the telephone, don't wait until the last minute (3 months after your birth month in which you turn 65) to find out what you need to do.