Umbrella insurance will not provide coverage for medical malpractice (most of the time the policy specifically excludes professional liabilities)
But it is useful for personal liability ... when you have a backyard get together (friends/family/coworkers) and something happens (deck collapses, dog bites someone, drowning in pool, fire/burn injury, etc). Also useful if you're involved in a MVA where you are deem at fault, and there are multiple victims (multiple hospital bills, or medical helicopters/trauma activation). Those liabilities add up fast, and can easily exceed most people's homeowner or auto insurance coverage.
More importantly, umbrella coverage comes with good defense lawyer since it is the insurance company's dime on the line ... the more at stake, the better the lawyer they will provide.
I pay roughly $20/month for 2 million umbrella coverage. That's a good price to pay for piece of mind knowing that I'm covered. The expensive portion of umbrella insurance isn't the premiums - it is upping existing coverage to the minimum required to have umbrella (most companies require a certain amount of liability coverage on auto/home before you can get umbrella)
Disability Insurance is always good to get (until financially independent) because you never know when you can't work ... whether due to illness, freak accident, etc. Please read the fine print. The residency plan of "60% of salary" may be 60% of resident salary (and not attending salary) ... so if you buy that plan without the option of increasing coverage in the future, coverage may be only 60% of what you made as a resident. It's better than nothing, but if you forget to review it or adjust it as an attending, getting 60% of resident salary instead of 60% attending salary is a big difference. There are riders that can increase coverage (and increase premiums) later on, without requiring medical exam, just need proof of income. If you are getting this plan as a resident, make sure you get this rider (and when you become an attending, increase your coverage when able).
Also make sure the disability policy is "own occupation" and not "any occupation". If you get disable and can't work as a doctor, but can be a cashier for Wal-Mart or a telemarketer, the insurance company would nto consider you disabled unless you have own-occupation definition.
Another thing that is good to have (esp as an attending, but also as a resident) is underinsured/uninsured motorist coverage ... if you get injured in an auto accident by someone, you'll have medical expenses. Sure, you'll have your own health insurance ... but there will be deductibles, copays for office visits/medications, lost wages (from not working, although disability should also cover that), plus struggles with prior authorization, denied treatment, etc. If you can get your car insurance to pay, there's less hassle - why spend any of your own hard work money or worry whether the anesthesiologist was in-network or out of network, whether the CT or MRI will be denied retroactively, or whether they will pay for home PT vs inpatient rehab, etc. However this type of insurance can be cheap or insanely expensive (depending on local markets, how many people have insurance, etc). Also depends on state as well (some state have medpay/personal injury policy) that may make this moot.