The most common concerns with electric vehicles are the range and the refueling times.
Refueling Times
Electric vehicles take 30 minutes to refuel at a super charger (which typically uses solar panels instead of the grid) and several hours at a typical wall outlet. This is not a problem if individuals simply charge their vehicles overnight. However, many people seem to think they will be driving long distances every day and will need to refuel often.
Range
Electric vehicles only have a range of around 250 miles or less, depending on the model or brand of vehicle. This creates a phenomenon called “range anxiety” among the general population. Although most people would not drive 200 miles in one day, individuals believe they will run out of charge on the battery and become stranded.
To combat this, Elon Musk, CEO and founder of Tesla Motors, released a software update for his electric vehicles that makes it impossible for the driver to run out of a charge. Essentially, the built in navigation accounts for the charging locations and won’t allow the driver to navigate somewhere so distant that he or she would be outside the range of a charger. If a driver only has 40 miles left on the battery, for example, the navigation system wouldn’t allow the driver to take a route to something 100 miles away without stopping at a charger first.

There are currently 3,542 super chargers in the USA with more being built every day. As more super chargers are introduced, range anxiety will decrease [1].
Sources used for this post:
[1] “Tesla Motors,” Tesla Motors. [Online]. Available at: https://www.teslamotors.com/. [Accessed: 07-Mar-2016].