I tried everything I could think of, short of replacing the microcontroller, and got nowhere. Finally I decided the board was safe and probably wouldn't kill my new chip, so I changed it out, flashed the firmware, and... it works! Hooray!

So what can we tell from this?

When you take out the screws which connect your electronics to the case, don't forget about the metal spacers. -and- Shorting the programming pins to ground on a sanguinololu board ends badly for your microcontroller.

Sigh... another day, another fun experiment in homebrew electronics. It's a good thing I'm not easily discouraged.

Did you say you have not put the metal spacers back in (the ones between the board and the case)?  If not, put them in.  I have had weird actions while working on the board with it powered on.  I think it is some strange grounding thing.  With the spacers out, crazy stuff, with the spacers in, everything fine.

The metal spacers are all back in and the board is screwed into place now. They were only briefly out during part of my playing with the extruder motor, so I don't think that's the root of the problem.

I've looked into it a little further, and shorting that 5v pin to ground shouldn't have done anything but make an internal fuse open until the short was removed. Probably. So I'm not sure I've done damage to my microcontroller.

Unfortunately it's now Monday, and I'm busy again, so this will probably go onto the back burner for a few days... but I'll update the thread with any new findings or failures at some point this week when I find time to play with it again.

After further playing, my earlier impressions were wrong. The speed the move is done at makes no difference to whether or not it's choppy.

However, I've discovered that the beats (or pauses, if you prefer) are regular like ronsii mentioned. They're not regular with distance traveled, though, they're regular in time.

No matter what speed you move at, the beats occur every 1/4 second (or as near as I can figure by tapping my toe to the beat and comparing against the second hand of a clock). So why would it be pausing in a pattern of 240hz (edit: my stupid mistake, it's pausing at 4hz or 240bpm)? Has the microcontroller been damaged?

While I was working on getting the new extruder attached I completely removed my electronics cover and, in the process, left all of the screws holding the board in place out. The double sided tape connection under the screw terminals seemed to hold it just fine. However, what I noticed (after applying power to the board, unfortunately) was that there are metal spacers under the board which aren't actually connected to the case as I had assumed. So... all three of them fell out, and in the process one wedged against the top two programming terminals on the board (the ones labeled 5v and Ground).

I immediately pulled power, saw no magic smoke escaping, and figured it was ok because on power-on the board responded and everything seemed ok. But now I'm wondering if the problem didn't begin then and I just didn't notice it for an hour or so because I was futzing with the extruder and not gantry motion (and the only thing I did to confirm that the board was still controlling things was homing the axes when they were already at home, meaning a short less than 1/4 second move).

I'm thinking I'll try reflashing the firmware and see if that works/fixes anything. But if that fails, or fails to resolve the problem, maybe I'll pop a new controller in. Luckily, I have an extra Atmega1284P with a bootloader and vanilla Marlin on it that I can try instead. Here goes nothing...

edit: ignore my earlier post about the power supply, if it was bad the sd lights would be flickering....

on the odd occasion I get the same thing. It is only ever during homing though (that I know of) and it hasn't seemed to affect any of my prints.

I had seen that too, this same choppy movement (without the high pitched noise and failure to move) when homing before starting a print and then the print is normal. Unfortunately, the current choppiness persists whether I'm manually moving things or it's running a print.

another thing I just thought of is the 12 volt powersupply if it is cutting out or not supplying enough power it could do this maybe a bad connection on the board, will it do the same thing with the bed and extruder off? I didn't get a chance to watch the vids yet.... I know ....just short on time as always

I haven't actually tested the motion with the bed or extruder on, all of this (videos included) is done with a cold bed and extruder. I haven't unscrewed, removed, and reattached the power connection but I did check it and it sure SEEMS to be in there as solidly as ever.

another thing I just thought of is the 12 volt powersupply if it is cutting out or not supplying enough power it could do this maybe a bad connection on the board, will it do the same thing with the bed and extruder off? I didn't get a chance to watch the vids yet.... I know ....just short on time as always

I wired it exactly the same way as the stock motor, but apparently color coded leads don't mean what I assumed they meant. Hitting extrude makes the motor run in reverse, and hitting retract makes it run forward. I figured I'd get around to fixing that when I got the bowden setup working correctly, but never got that far.

I don't think this could be related, though, because everything was working normally for at least an hour with the extruder motor wired backwards. But hey... this is so weird I figured I'd throw in all the details in case I'm missing something simple.

The x-axis - http://youtu.be/0p4aRBZ6jn0

Notice that even when it is moving smoothly, that motion ends with a loud clunk. That only started when the choppy motion started.

The y-axis - http://youtu.be/DyUIAt6Bl0A

This is where I managed to catch the high pitched buzz and failure to move.

The z-axis - http://youtu.be/n2L_ojsKLa8

Even the Z does the choppy motion.

Also worth noting, in making the videos the printer was connected to an entirely different PC from the one it was on earlier this evening when I first started seeing this problem. There didn't seem to be any difference in performance.

It's a long shot, but try cooling the drivers if you aren't already.  Maybe they are going into thermal shutdown.

How is the Z axis doing?

The drivers shouldn't be overheating, they each have a heatsink and there's a 50mm fan blowing on them. It shouldn't be a problem with heatsink adhesion either, those have been on for about a month now, and I used thermal epoxy to attach them so they can't have shifted or come loose.