What special skills are needed to play the accordion?
By coming to this website, you've already demonstrated curiousity and the ability to seek out information. These are good qualities for learning any musical instrument, especially the accordion. Many believe music is a special gift that one inherits while others believe it is acquired by being born to a musical family or at least by being in a musical environment at an early age. Some call it talent while others call it developed skill. Regardless, music comes easier for some people, just like math, tennis, bridge and computing. This NEVER means you don't have the talent; rather, it means you may need to strive a bit more to master the skill. One does not need to be perfect at everything. In fact, it's okay NOT to be perfect at everything but, rather, to be merely competent.
This said, then, motivation is needed to learn the accordion. You must want to do it and be willing to stick to it for six months to a year in order to be reasonably competent. It does not happen overnight. It takes some commitment and ability to stay on task and practice daily.
In addition, you have to be strong enough to hold the instrument as well as to have the basic coordination to push and pull the bellows while playing the keys and buttons with your right and left hands. Most people do have this coordination, if not at the beginning, later in their development.
Individuals who already play a musical instrument and can read music are at a special advantage from their experience and learn the accordion in shorter time. If you have to learn to read music while you're navigating all the mechanisms on the instrument, it takes longer.
Oh, yes, you need a good sense of humor and the ability to laugh at bad jokes at your expense.