Off the top of my head, sounds like there may be low voltage arcing SOMEWHERE in your wiring system; affects digital, computers, etc., more than resistive or motor loads so its hard to pin down, i.e. a light plugged into the offending outlet might not dim down enough to notice a problem.
A good place to start is to check that the phase conductors in your panel are tight with no insulation on the lugs. You have to be able to see a little copper underneath.
Also, check the new wiring - some electricians do not strip back new wires far enough; they push them down to expose the copper, install them, and then the plastic jacket pushes up and dislodges the copper connection if they aren't tight. Check those on the new circuits, especially the neutrals (white). Also, take your multimeter and check the voltage drop across the breakers (careful!!). Good luck, these problems are a royal pain.