Number of Networks
When the Internet was designed it was to have about 50 connected networks. With the explosion of networking, the number is now approaching 300. The software in a group of critical gateways (called the core gateways of the ARPAnet) are not able to pass or store much more than that number. In the short term, core reallocation and recoding has raised the number slightly. By the summer of '88 the current PDP-11 core gateways will be replaced with BBN Butterfly gateways which will solve the problem.
Routing Issues
Along with sheer mass of the data necessary to route packets to a large number of networks, there are many problems with the updating, stability, and optimality of the routing algorithms. Much research is being done in the area, but the optimal solution to these routing problems is still years away. In most cases the the routing we have today works, but sub- optimally and sometimes unpredictably.