Here is a a thought...
Assuming that you wired them correctly.
If you slide a pot and the values of the other pots change... that means to me that it is very likely that your 5V power source changed voltage... IE; the "load" caused a change in regulated voltage and as a result... it changed all the voltage levels seen by that analog pins accordingly. If you have a voltmeter, you might be able to confirm this by monitoring your power rails while you make adjustments. It will either remain stable (good) or raise and drop a little (bad).
Bad means... maybe you need a better voltage source.