Independent analog sensors have dependent readings?
There are a lot of things that could be causing this problem.  see here.  However, what appears to be the most obvious is a problem with sampling time.

If you check out page 35, it mentions that the ADC is a sample and hold converter:  it has a capacitor that charges (or discharges) until it has the same voltage as the source, then it reads that value.  The time for this is set by the time that SW1 is on: the "sampling time".  If there isn't enough time for the capacitor to discharge/charge to the correct voltage before turning off the switch and reading the value (depending on the resistance of the source), then you won't get the right value.







simulate this circuit &ndash; Schematic created using CircuitLab

This is in the section on problems with reading high impedance sources.  The LM35 has a low impedance output if it is sourcing current, it can only sink 1µA of current though, which makes it a very high impedance current sink.

If you are setting a higher voltage with the pot than you are reading from the LM35, then the current from the capacitor needs to flow out of C_sh through the LM35:  this is very slow (because of that 1µA current sink capability), and thus your sampling time is too short.

A capacitor helps to smooth this out, but also slows down the response time of the LM35.

A quick fix is to put a >1kΩ resistor in parallel with the LM35.  This sinks current when you need it to, and gives a current path to ground for the current from C_sh.