I've done it a little. Nothing large scale, just small stuff for low voltage electronics.
Usually its not a cost saving option. Economies of scale generally mean that you end up paying more for components than you would for an assembled unit. Its the same reason that its more expensive to buy an entire car's worth of parts instead of a brand new car.
The connections are usually super thin wires between individual cells. If you're pretty good with a soldering iron, then you can definitely do it but, it can be tricky. Manufacturing processes usually use either CNC machines or manually controlled special application soldering devices. If the connection isn't great, then it can break with the thermal cycling associated with being out in the sun. You should be using a series/parallel arrangement in your overall panel so that each series of cells increases your voltage and your parallel arrangement increases your current. If you break a connection you would still have your same voltage output, but a lower current.
The main positive to me is the simple satisfaction in building something yourself. If I can build something myself, and I have the time and its not much more expensive, I'll always built my own stuff. Its way cooler. The other advantage in my mind is footprint optimization. If space is at a premium, you can't always chuck a big rectangular panel onto your round gazebo roof, etc... Being able to build your own shape will allow you to work around trees, antennas, chimneys, etc... and still give one panel.
If anyone else had any thoughts about this, I'd be keen to hear them