CONS - it takes a mindset change to get used to not having a 'base'. A place to call home except the RV. Having spent 20 years in the US Navy moving around often it wasn't as big a deal to me as the wife.
Doctors - that is a solvable problem, but you would have a physician like my wife has - whose staff can't seem to get over sending prescriptions to the local pharmacy. You need to talk with your doctors and make sure they understand you plan to be in to see them only once or twice a year. A full-timer might need to change their primary care and specialists doctors to a location they plan to visit every year, and who understand/ have experience with the RV lifestyle.
Health Insurance - If you plan to travel across the country, and are not on Medicare or another national health insurance plan - check with your provider. Many folks have policies limited to a small region or their home state.
Internet - It is costly and somewhat unreliable when full-timing. Don't count of RV park internet or free WiFi. You are going to have to have a phone company plan, and have to be careful with your usage so that you don't go over your plan limits. If you plan to visit some of the scenic wilderness in this country - you will be without any internet (or phone) access for days at a time.
Maintenance - as mentioned above - you will always need to adjust/ fix something. It isn't a 'quality' of the RV issue. Thousands of miles per year on the rig makes things work loose. A bigger issue for you might be access. Things are so close together in an RV, that working on anything gets difficult.
Holidays - we live in a 36' TT towed by a 3/4 ton truck. We've traveled over 25,000 miles, camping in 29 different states. We only reserve a campground spot about 1/3 of the time. But we have learned we need to plan our stops for holidays and book several weeks in advance. Memorial Day, Fourth of July, Labor Day, Thanksgiving Week, the week after Christmas - we've been shut out of preferred campgrounds on those. (And be wary of spring break season if you plan to be anywhere near a warm beach.)