Attached is a picture of my current 4-layer PCB layout surrounding the LM3940. Via holes are 12mil. On the input line there is a 0.47uF MLCC. On the output line there is a 47uF (!6.3V) tantalum capacitor. Are the thermal relief connections problematic? Assuming that the ground plane is well "stitched" (it should be stitched with the internal ground plane right?), is the grounding for the regulator OK? What about the 5V in and 3.3V out? To me it looks kind of hackish (which I guess it is).
In front of the LM3940 there is a DC/DC regulator that has an output ripple Pk-Pk of 27mV. The LM3940 DS states that the input voltage has to be well regulated. Is this well-regulated? If not, what capacitors would you suggest adding to the input. The DS only specifies low ESR for these capacitors, not the capacitance.