First off, thank you very much to all who responded, I really appreciate it.

I probably should have included some more details in my original post.
I am indeed using the HiTech PICC compiler, and my circuit does have
capacitors coupled between the individual a/d inputs and ground.

As far as my delay routines, they were taken from an example in Myke
Predko's book, 123 Pic Microcontroller Experiments for the Evil
Genius.  I will take a look at the example delay routines included
with the compiler.

An interrupt approach ulimately solved my problem, which is something
I wouldn't have readily considered as a solution, so many thanks for
that advice.  I am still a little confused as to why the interrupt
approach worked as opposed to a modifed polling type approach simmilar
to what I tried first.  No matter how much time I allowed after
switching a/d channels, subsequent reads always produced the same
values, regardless of the inputs changing.

Anyway, I have attached the latest (working!) code in hopes that it
might help someone else someday.

Thanks again,
Jason

/**
ThermInt.c
Jason Wambach

Use interrupt based ADC to read temperature from thermistor and set
point from pot

**/
#include <pic.h>
#include <math.h>
__CONFIG(FCMDIS & IESODIS & BORDIS & UNPROTECT & MCLREN & PWRTEN &
WDTDIS & INTIO);


int i,j,k,n,b,sw;
unsigned int a;
double Temp;
//                          1234567890123456
const char TopMessage[]  = "Curr Temp: ";
const char BotMessage[]  = "Set  Temp: ";

#define E RC4
#define RS RC5

const int Twentyms = 1250;

const int Fivems = 300;
const int TwoHundredus = 10;

//4bit LCD Write Operation
//Tell the compiler that this method cannot be called from 2 locations
//at the same time
#pragma interrupt_level 1
LCDWrite(int LCDData, int RSValue)
{
	PORTC = (LCDData >> 4) & 0x0F;
	RS = RSValue;
	E = 1; E = 0;

	PORTC = LCDData & 0x0F;

	RS = RSValue;
	E = 1;
	E = 0;

	if ((0 == (LCDData & 0xFC)) && (0 == RSValue))
	{
		n =  Fivems;
	}
	else
	{
		n = TwoHundredus;
	}
	for (k = 0; k < n; k++);
	
}

//Write formatted decimal to LCD
TempDec(int i)
{
	int t;
	
	if (i >= 100)
	{
		t = i / 100;
		LCDWrite('0' + t, 1);
		i = i % 100;	
	}
	else
	{
		LCDWrite(' ', 1);
	}
	if (i >= 10)
	{
		t = i / 10;
		LCDWrite('0' + t, 1);
		i = i % 10;
	}
	else
	{
		LCDWrite('0', 1);
	}
	LCDWrite('0' + i, 1);
}

void updateLCD()
{
	LCDWrite(0b00000001,0);  //clear lcd
	for (i = 0; i< TopMessage[i] != 0; i++)
	{
		LCDWrite(TopMessage[i],1);
		//LCDWrite('0' + i, 1);
	}
	
	TempDec(a);  //Format and display
	LCDWrite(0xDF, 1);  //Degree symbol
	LCDWrite('F', 1);

	LCDWrite(0b11000000,0); //Move to 2nd line
	//2nd Line
	for (i = 0; BotMessage[i] != 0; i++)
	{
		LCDWrite(BotMessage[i],1);
	}
	
	TempDec(b);
	LCDWrite(0xDF, 1);
	LCDWrite('F', 1);
}

#pragma interrupt_level 1
void interrupt adint(void)
{
	if (sw)
	{	//Thermo
		a = (ADRESH << 8) + ADRESL;
		
		//Temperature Calculation
		Temp = (1023.0 / (double)a) - 1.0;
		Temp = log(Temp);
        	Temp = 32.5 - (Temp / 0.019129);
		Temp = (9f/5f)*Temp+32;
		a = (int)Temp;
		//set for pot read
		ADCON0 = 0b00001001;  //select RA2, Left justified result
		updateLCD();
	}
	else
	{
		b = ADRESH;  //only care about 8 most significant bits
		b *= 30;
		b /= 255;
		b += 60;  //Want b in the range of 60-90
		//Control an led on RA4, eventually control a relay connected to heater
		if (b <= a)
		{
			RA4 = 0;
		}
		else
		{
			RA4 = 1;	
		}
		//setup for temp read
		ADCON0 = 0b10000001; //Selected RA0, Right justified
	}
	sw = sw ^ 1;  //Flip Flop between AD Channels
	ADIF = 0;     //Reset AD Interrupt Flag
	GODONE = 1;   //Start AD Again
}

main()
{
	PORTC = 0;
	CMCON0 = 7;
	TRISC = 0;
	TRISA0 = 1;
	TRISA2 = 1;
	TRISA4 = 0;
	ANSEL  = 0b00000101;
	ADCON0 = 0b10000001;	
	ADCON1 = 0b00010000; //Clock Fosc/8 or 2uS
	
	//LCD Initialization
	j = Twentyms;
	for (i = 0; i < j; i++);
	PORTC = 3;
	E = 1; E = 0;  //Reset
	j = Fivems;
	for (i = 0; i < j; i++);

	E = 1; E = 0;  //Reset 2
	j = TwoHundredus;
	for (i = 0; i < j; i++);
	
	E = 1; E = 0;  //Reset 3
	j = TwoHundredus;
	for (i = 0; i < j; i++);

	PORTC = 2;
	E = 1; E = 0;
	j = TwoHundredus;
	for (i = 0; i < j; i++);
	
	//Only called before interrupts are enabled
	LCDWrite(0b00101000,0);
	LCDWrite(0b00000001,0);  //clear lcd
	LCDWrite(0b00000110,0);
	LCDWrite(0b00001110,0);

	a = 0;
	b = 0;
	sw = 1;

	//Enable interrupts
	PEIE = 1;
	GIE = 1;
	ADIF = 0;
	ADIE = 1;
		
	GODONE = 1;  //Start AD

	while (1 == 1);
}

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