A while ago I saw a protoboard with the pads all connected; at the time I thought it was a manufacturing glitch, but today I saw another one. I cannot think how these boards may be useful - any ideas?
That perfboard doesn't have its pads connected. It has no pads, since there's a clear area around each hole.
Instead it has a plane with a void for each hole. You could use this plane as a power or ground plane, while making other connections with wires between the pins of the components in your circuit.
Those are usually used as ground and power planes. These printed circuit boards are usually used when prototyping using wire wrap sockets.
Through hole devices like wire wrap sockets do not touch the copper traces. The builder purposely connects the power plane to the power pins of the sockets where necessary. In addition to distributing power, such planes help reduce noise by acting like shields.
This board is a bit messy. But you can see where there is a gap around each pin. So the builder can choose to or not to connect a pin to a power plane.
I have seen people take a knife to these kind of boards and manually etch off paths to create a prototype circuit. Generally this only done when they don't have a breadboard handy or ability to get a real board printed.
It's a pretty quick and dirty solution but it has come in hand to test components fitting together and circuit designs.