The growth in CPU, memory and storage performance/price has made possible all these new applications. The reduction in connectivity costs is leading to the use of these new applications. The corresponding increase in network functionality has yet to happen. The Internet is experiencing a number of problems due to the growth in its size, and in breadth of the community using it. These include:
The number of systems is exceeding the available numbers for addressing systems in the Internet - a similar problem that everyone in the UK is accustomed to from time to time with telephone numbers. The way these numbers are allocated is also leading to problems with the amount of memory in the router boxes that hold together the Internet. Currently, these need to hold the full list of every site in the Internet. A more hierarchical approach (like the phone system or the postal system) will fix this.
Security is really not a question that is relevant when talking about the Internet itself. What needs to be secured are hosts, and information. However, the network must provide relevant hooks for security to be implemented.
Currently, the charging model in most of the Internet is a leasing
one. Bills are for the speed of access, not the amount of usage.
However, many believe that at least during busy periods, or else for
priority service, billing will be necessary as a negative feedback
mechanism. This will also require security so that the right people
can be billed legally. 
The Internet has not historically provided guarantees of service. Many providers have done so, but typically by over-provisioning the internal resources of their networks. In the long run, this may prove viable, but at least for the next few years, we will need mechanisms to control guarantees, especially of timeliness of delivery of information. For example many information providers such as the Share Trading and News businesses value their commodity by time.