What the output isn't correct when I use a switching power supply?
First, that REG1117 is a linear regulator, not a switcher.  It seems to be connected correctly.  The 100 &micro;F and 100 nF caps on the output make sense.  The 220 &micro;F on the input makes sense too, but something will low impedance at high frequencies is missing there.  USB allows up to 10 &micro;F on the power line, but even just a 1 &micro;F ceramic immediately across pins 3 and 1 of the regulator should be all that is needed.  Check the regulator datasheet.

Another problem is the lack of bypass caps for the microcontroller.  None are shown.  There are two caps off in the lower left corner for no apparent reason, but I count 5 power pin connections, so two caps is insufficient even if that's what C7 and C8 are (in which case they should be labeled as such on the schematic).  Not only should there be one per power pin, but they must be physically close to the power and ground pins.  Note that there is a ground pin adjacent to each power pin.  One cap needs to be close to the chip across each pair of power/ground pins.

Another issue is that 32 kHz crystal has no load caps, but that unlikely has any bearing on the symptoms you are reporting.

The procedure for debugging this is to look at the power voltage at each power pin.  Also make sure each ground pin is really at ground.  A small break in a ground connection can cause all manner of trouble.