Double clicking is more of a problem on touch screen devices (or even just cheaper laptops) where the finger or a stylus is used instead of the easier-to-double-click mouse.
The problem is some people suffer from (Pam Martin's) Double Dysclicksia - as argued by Jef Raskin in The Humane Interface. New Directions for Designing Interactive Systems (Chapter 4.2) From which I quote:
The interface technique called double clicking, that is, tapping the GID button twice within a small time window and without any significant cursor movement between the taps, as an interface technique suffers from problems. You cannot always predict what objects on the display will or will not respond to a double click, and it is not always clear what will happen if there is a response. There is no indication on displayable items that double clicking is supposed to produce a response: The functionality is invisible. The way that double clicking is used in many current interfaces, the user must remember not only which items are double clickable but also how different classes of interface features respond to this action.
The first two burdens on the user could be at least partially alleviated by new screen conventions. The act of double clicking is, however, itself problematical. Double clicking requires operating a mouse button twice at the same location or at two locations in very close proximity and, in most cases, within a short time, typically 500 msec. If the user clicks too slowly, the machine responds to two single clicks rather than to one double click. If the user jiggles the mouse excessively between clicks, the same error occurs. If the user taps the GID button twice in too short a time period, as when trying to select text within a word while working within certain word processors, the machine considers the two taps as a double click and selects the whole word.
A problem arises when the user is trying to select a graphical item that can be repositioned with the GID. Because the GID is likely to move when the user is pressing the GID buttons quickly, graphical applications, instead of reading a double click, may read a drag-and-drop and change the item's position. Similarly, to change the text in a text box, the user may find it necessary to reposition the accidentally moved box and to make the text edit originally intended.
Some of us are unaffected by dysclicksia: These lucky people never miss with the mouse; they single and double click with insouciance and panache, do not suffer from side effects of clicking, always remember what will and what will not respond to double clicking, and can shoot a flying bird with a .357-caliber revolver while driving along a twisty mountain road. But we can't assume that all users are so lucky. We must design for the dysclicksic user and remain aware of the problems inherent in using double clicks in an interface.