The biggest problem HTML5 is supposed to solve is write once run anywhere applicatons. Most of the programs will have the same look and feel if they are run on a PC or mobile and between different devices.
Ofcourse not everything is perfect. There are yet many API's that need to be implemented in for HTML5 like the 3D and Mic API's, etc. Another problem is that a lot of phones are not yet supporting HTML5 and some of them that are supporting, not supporting it completely. This will have to be solved asap.