Good point, Hood. If the screen is showing the correct tool path (you can check this also on the "Tool Path" screen which has a much larger image to view) then it is most likely a trouble with the machine itself and not Mach3. So switching to Mach4 wouldn't help. Mach3 is still a good viable program to use. I have not seen a need to change to 4 myself so let's figure out what is going wrong instead of adding another variable to the mix.
Since it sounds like your Y axis is the one having trouble based on what I'm reading in this thread, could you try swapping the X and Y motors? If you do that and the symptom changes to the X axis then it's the motor. If it stays with the Y axis then I suspect electronic noise is the culprit. Proper grounding cable/wire routing is the best way to deal with that and there are whole discussions around eliminating noise. I am much less than an expert in this area so I would differ to others to chime in on that. So try the motor swap if it's not too difficult on your machine and let us know what you find from that.
The one thing that bothers me is that Auto Zero issue you had. This still sounds like a DIR line issue, but with a different axis. You may have to adjust the Step Pulse setting in the Motor Tuning screen. What it sounds like now that I think about it is that the step pulses may be starting too soon after setting the DIR line high/low (depending on direction) and the stepper driver does not have a chance to sense the direction change before starting the motor spinning. Most stepper drivers have some minimum required delay between changing the DIR signal and receiving the first pulse on the STEP line and if the first pulse occurs too early it could spin the motor in the wrong direction briefly. This would account for the .150 difference in your Y zero operation and would also account for the brief push down before retraction on your Auto Zero operation.
Keep us posted on your findings,
Stephen "Highspeed" Kruse
EDIT: While posting this, I see Hood also replied. Hood, what are your thoughts on that DIR/STEP timing I discussed above?