For microcontrollers themselves most faults come from insufficient datasheet reading. Most of the time something doesn't work as intended the reason is that you forgot to set some register. Modern MCUs are very complex devices with tons of options and it's very hard to remember about them all. Moreover - they often collide with each other. So the most commom failure mode is IMO software bug.
Another vital thing is powering. Most MCUs have several power and ground pins, all of which have to be connected. They also should be decoupled well, according to the datasheet. Analog voltage supply, if the device has one has to be properly conditioned (ideally whole separate power supply for analog purposes). Datasheet usually contains detailed info about minimal operation setup. Example:
https://ww1.microchip.com/downloads/en/DeviceDoc/39897c.pdf page 27 and forth.
Another common problem are wiring mistakes. While on veroboard this is not a problem, if you order a pcb made or etch it by yourself the connections are hard to change. In some cases you can apply some hack involving rotary tool, sharp knife, fine magnet wire etc, but not always.
PCBs can have manufacturing faults, like a break in a track. Such breaks are often microscopic and almost impossible to spot with bare eye. If your board is somewhat experimental you may want to place large number of test points which make testing, debugging and development easier. Some mistakes also come from erroneous libraries in cad software. They can have pins mixed around or (more likely) you will choose wrong footprint, which may render whole board impossible to assemble.
On veroboard most common failure mode are cold joints, broke leads and so on. I personally don't use veroboards, other than for really simple things (like 5 buttons forming a keyboard).