Everything I look at my engine from the pass side it seams like it is closer to the pass side than the drivers side.

|UPDATED|9/28/2012 3:39:06 PM (AZT)|/UPDATED|

I kind of did when I put my motor in this summer.  I initially used cheaper parts store motor mounts and ended up having all kinds of trouble lining things up.   The problem was that the mounts were much wider than the frame brackets, thus allowing too much play.  I actually got up above and in front of the engine bay (hood was off) and could see that it was cock-eyed.  Solved the problem by taking back the cheapo mounts and installing a set of Energy Suspension mounts that fit perfectly.  Not sure if this could be causing your issue, but maybe....

The engines on C3's were offset to the passenger side by little over 1".

From the things I read over the years, some say it was to compensate for drivers weight. Then some say it was to allow for extra foot room on the drivers side for the pedals.

I would think it was to allow room for the steering box. There ain't much there.  I can attest to that since I was putting a new Borgeson steering box in my vette last night.

Yup....the engines/drivetrains are off-set to the pass side, to clear the steering box, and the cars were designed that way even before the big blocks came into play. Remember, the chassis was designed waaaay back for the '63 cars.
It also helps with clearance for the transmissions, especially 4 speeds, and their linkages.

Never paid much attention to the engine, but know the transmission sets closer to the tunnel on the passenger side. Not much room for the aluminum heat shield and the speedo cable.

Thats just WRONG!

Something doesn't look right based on that picture, unless it's just from the camera angle.  I'd look more closely at those motor mounts.  

The rear end is on center, the drive shaft u-joints make up for the offset.

The pic looks weird, I'll give ya that. but it's hard to really tell from a pic. It's possible the trans mount is off/broken, and that could cause the front of the engine to shift farther to one side or the other.

As far as the mechanics of moving the drivetrain to one side or the other, it has to be "in line", meaning if the front of the engine is moved over, the trans has to move over the same amount. As long as the differential yoke is parallel to the centerline of the engine/trans, it poses no problems. If, however, the engine/trans is angled, and the diff yoke is NOT parallel, you wind up with some serious driveline vibrations. U-joints are designed to allow the off-set of drivelines, without binding. IF the angle of the trans, and the angle of the diff are off, it will vibrate. It doesn't matter if the centerlines are off....the problem is the angles.
So, if, for instance, say the trans mount is broken, and the rear of the trans is shifted to one side...the driveshaft will vibrate because the angles are off.
If you simply move the engine/trans to one side and equal amount, and the engine/trans is aligned front/rear, there will be no problems with vibrations, as the u-joints will work as designed. Think of a regular, rear wheel drive vehicle...the diff moves up/down as you travel over bumps/dips. By design, the angle of the diff yoke, and the angle of the tailshaft of the trans is the same, or within a couple of degrees of each other. This makes the u-joints work properly, and not have any driveline vibrations. IF, however, you wanna jack up the suspension on yer 4x4 truck, you mess with the angles between the trans and the diff yoke...and you get vibrations, and u-joint bind. On 4x4s that are jacked up, the diffs usually have wedges installed on the springs, to return the diff yoke angle back to "normal".
Same problem if you used air shocks back in the day to jack the rear of your Chevelle up...you effectively changed the angle of the diff, and it makes the u-joints work hard to keep the driveshaft spinning smoothly...and they usually failed much sooner than they would have normally.

Bottom line is, as long as the angles of the engine/trans, and the diff yoke are the same, there will be no problems with the driveline. On our model Corvettes, the engine/trans is offset to one side a small amount, but on a straight line front/rear. Also, the height of the trans and diff do not change...they(the angles) stay the same, so the only work the u-joints do is for the side/side offset. Not a problem.

Hope this helps, and is not even more confusing. I ain't that good at 'splaining stuff like this...it's easier for me to show how it works, than describe how it works. Good thing I ain't a teacher....