Well, the coin hit coming up with nothing, or a nail is not uncommon. Iron objects, if they are on end especially can fool some detectors. Coins, will OFTEN seem to disappear as you dig them... either they get flipped on end which makes them disappear, or they fall from the side of the hole down deep into the hole where they are out of range... best thing to do is take a few more scoops, then spread the dirt to make sure it's not on end.
As for the erratic behavior, that isn't normal. My 350 did act up once in awhile... it would start beeping like mad just random hits all over the place. I found that it only did it in my back yard... near the power lines.
Also, when the batteries got low it would do it also.
If you have tried multiple locations and still need to run the sens down that low it very likely has an issue. Mine never went nuts when I was digging unless my blade or pinpointer was within range.
Speaking of interference.. once time I was playing with a solar panel connected to an audio amplifier. I pointed it at my laptop screen and got clear audible data... like a modem ... I recognized the sound of it. It was the (other) HAM radio operator 3 blocks from me doing RTTY (an early digital radio mode).
His transmission was either modulating the power (less likely but possible), or my lcd screen was picking up his transmission like an antenna (more likely). It came in clearly as optical modulation on the solar panel but you could see nothing unusual on the screen.
RF noise is everywhere even where you don't expect it.