I own a 2007 GS500F.  Everything is stock.  It currently it has about 1600 miles on it (I bought it with only 1100 miles on it).

My bike has been running very lean.  So lean that I have a hanging idle (When I close the throttle, the RPM's do not immediately drop like they should).

So recently I decided to pull the carbs out to clean them and shim the needle with two #3 washers.  Now that it's back together, I have a new, much more distressing problem:

When I start the bike with choke, it revs up to 4000 within a few seconds, and then I drop it down to about half choke.  Then it idles very ROUGHLY at 1500-2000, and then periodically makes a very loud POP, like a shot from an air rifle.  It's coming from the front of the bike, not the exhaust.  It's also accompanied by a faint burning smell.  (possibly electrical?? I don't really know)  When this pop occurs, the RPM's drop, and it usually sputters out and dies shortly after.

I'm going to open it back up and pull the washers off the needle to see if returning it to stock fixes it, but I have a feeling it won't.  [UPDATE: returning it to stock did nothing to solve this problem]

Anyone have this problem before or know what I did? 

A few updates:  I removed the two washers and it is now exactly like it was before I pulled the carbs out.  No change.  Problem still occurring.

The POP is more like the sound of an air rifle, not a gunshot.  It does not occur if I leave full choke on.  It only occurs when the choke is at half or less when the bike is idling at less than 2500 rpm's. 

When the POP's occur, there is a large RPM drop.  Bike usually sputters out and dies shortly after.

POP sounds like it's coming from the LEFT side of the bike, though I can't be sure.

Maybe a backfire from the carbs? I suppose one could remove the filter and run it for a short while and see if that is where the sound is coming from.

Are you able to ride the bike after the engine warms up?

I experienced backfiring (popping backwards through the carbs) and stalling when one of my ignition coils failed.  Running on one cylinder caused a drastic loss of power.

PS the captcha verification goes away after your fifth post.

Looked up a video of carbs backfiring.  It sounds VERY similar.  Is it safe to start it up for a short time without the airbox?

Yes, i was able to ride the bike after it warmed up and didn't experience any sounds while riding it. I just left the choke on while riding for the first 5-10 minutes then it was ok to take off. 
It idled very low and I thought it was going to stall a few times, but it did not. 
Taking off after stops seemed very sluggish/bogged down. 
Power while cruising was not noticably different.

After it sat for about half an hour, I started it back up again and am experiencing the 'POP's again.

I'm sure I caused this problem when reinstalling the carbs, so unless there's something I could have done to cause my ignition coils to fail, I don't believe that's the problem.

I'm thinking vacuum leak?

Running it without the airbox is about the only way to see your slides, just don't make a habit of leaving it like that. Have you checked the lines going to the nipple caps? I had to repair a nipple with epoxy and a new nipple.

I'm a novice mechanic.  Never even did my own oil change before my wife and I bought bikes, lol.

The nipple caps are the white-ish plastic on the tops of the carbs, right?  There are two nozzles on each.  The left side nozzle on each carburetor is uncapped.  Is this normal? I checked my 'before' picture, and that's how they were before I pulled the carbs.

The attached hoses on the right side nozzles look fine.  They're tight and no holes that I can see.  Not dryrotted.

SOLVED!

Had a pretty severe vacuum leak around the rubbers between the engine and the carbs.  As soon as I fixed that, no more carb backfires.

Re-shimmed my carb needles with the two #3 washers, and now my bike idles normally again too.  No more hanging idle. Though I still believe it's running a bit lean.  Maybe I'll rejet it at some point.

Were your boots cracked? Loose?