Yes, calibration will help with clearing up the pictures in both cases. As mentioned in other threads about these discs, some sources may come out looking better while others look worse. In other words, calibrating your DVD might make incoming broadcast reception look unnatural. You'll have to try it and see. I do know that a few tv's have individual calibrations for each input, giving you the ultimate in versatility and viewability.
As to moving an RPTV, that can throw a LOT more than just the calibrations out of whack. If not careful, you would have to have the guns re-aligned. Like with any other big and expensive gear, simply take your time and be careful. I haven't experienced any problems when having to move the TV for rewiring or cleaning.
Something to keep in mind that is not often discussed is that some RPTV's allow you to set the "convergence" via the remote while others don't. You'll have to read the manual and see. Either way, i don't think that anybody would want to abuse their tv to the point of throwing it completely out of whack.
The biggest problem with "calibrating" the tv's is that, when you lose power, your tv will reset itself to the factory defaults. Then you have to recalibrate all over again. As mentioned in another thread, you might want to take some quick notes as to where the settings are at so that you can "rough" things in without having to go through a complete "calibration" procedure using the disc again. Sean