Bicycle Tutor

(It was hard to come up with a title for this one)
A while back my rear derailer was autoshifting and/or skipping, esp under load and i couldn't figure out why. After awhile it stopped, and I never really put together why it started or why it stopped: until today.
Today I decided to flip my bike (no repair stand yet) and check my tires for glass working it's way through the tire since I've ridden over glass a few times in the last few days. I found some glass and fished it out, but couldn't tell if there was still a fragment in there so I took my wheel of my bike (etc)... When I went to put it back on I was playing around with tension of the quick release skewer and noticed that tightening them made the the frame visibly bend made more apparent by how much it made the derailer move sideways. Thinking that bending my frame every time I remove/install the wheel is probably a bad thing I went with the light tension and sure enough 10 feet down the road and I was getting off and tightening it again so that I could shift properly/didn't get random skips.
So: is this frame bend really an issue, and how can I ensure that I'm clamping the quick release to the same pressure every time so as not to put the derailer out of alignment?
(it should be noted that I've had this bike 4 months and have not checked this derailers cable for stretch nor checked the adjustment of the derailer, still it runs fine if the wheel in tightened)

It sounds like the derailleur is shifting position which would definately cause jumping between gears. But the bigger question is why/how your frame is "bending" when you tighten you QR. It really shouldn't do that. Does your derailleur screw directly into the frame or does it have a hook that sits under the QR? Sounds like something is misaligned if tightening the QR is flexing the frame.