Calculating totals returning error if any cell is empty.

When the field is empty it returns an empty string (""). The "+" operator is used to both add up numbers and to concatenate strings. So when the script sees that one of the values is a string, it defaults to treating them all as such, and therefore the values get concatenated.
The solution is simple: force the script to treat the blank values as a number (0), by placing a Number() constructor around them, or simply a "+" before them (another use for it!), like so:

var f0 = +this.getField("txAmount0").value;
var f1 = +this.getField("txAmount1").value;
var f2 = +this.getField("txAmount2").value;
var f3 = +this.getField("txAmount3").value;

Thank you very much try67, your solution worked perfectly :-)

Now then, one extra little question:

The extended script I use on the form has 21 fields, so the calculating script looks like this:

-----------------------------------------------

var f0 = +this.getField("txAmount0").value;
var f1 = +this.getField("txAmount1").value;
var f2 = +this.getField("txAmount2").value;
var f3 = +this.getField("txAmount3").value;
var f4 = +this.getField("txAmount4").value;
var f5 = +this.getField("txAmount5").value;
var f6 = +this.getField("txAmount6").value;
var f7 = +this.getField("txAmount7").value;
var f8 = +this.getField("txAmount8").value;
var f9 = +this.getField("txAmount9").value;
var f10 = +this.getField("txAmount10").value;
var f11 = +this.getField("txAmount11").value;
var f12 = +this.getField("txAmount12").value;
var f13 = +this.getField("txAmount13").value;
var f14 = +this.getField("txAmount14").value;
var f15 = +this.getField("txAmount15").value;
var f16 = +this.getField("txAmount16").value;
var f17 = +this.getField("txAmount17").value;
var f18 = +this.getField("txAmount18").value;
var f19 = +this.getField("txAmount19").value;
var f20 = +this.getField("txAmount20").value;

event.value=f0 + f1 + f2 + f3 + f4 + f5 + f6 + f7 + f8 + f9 + f10 + f11 + f12 + f13 + f14 + f15 + f16 + f17 + f18 + f19 + f20;

if(event.value==0)
event.value="";
---------------------------------------------------

Is this the best format of the script or is there a more efficient (shorthand) format that can be used?

No problem as it is, just wondering :-)

Something to remember when dealing with Acrobat calculations I have just discovered.

After replacing the 'Value is the...' script with the Custom Script above, my 'Total Return' script began to return 10 fewer than it should!

Then I checked the Calculation Order (Forms > Edit Fields > Set Field Calculation Order...) and discovered the TotalSpent and the Return fields had swapped round.Reordering the fields correctly for the calculation, fixed it.

Trap for young players, I was lucky I had read something about that issue earlier in the day or I would have been stumped...again!

You can reduce the size of your addition script by using a control loop and computing the field name. You can also use the Number constrictor to force a null field to the number zero. Using a function will also reduce the run time of the script.

(function() {
var Sum = 0; // variable for sum
// control loop to sum fields
for(i = 0; i < 20; i++) {
Sum += Number(this.getField("txtAmount" + i).value); // add i field
} // end for loop
if(Sum == 0) Sum = ""; // null value if Sum is zero
return Sum; // return result
}) (); // run function

Using the unary + operator as try67 showed is generally the fastest way to convert a string to a number, while using the Number constructor is equivalent in outcome but is generally the slowest method. Unary + is also results in smaller and more readable (IMO) code, but some find the Number constructor is more clear and worth whatever speed penalty there may be. For more info, see: http://jibbering.com/faq/notes/type-conversion/#tcNumber

Consider this, as well: If all you're doing is adding up these fields, you might as well use the built-in method for doing that ("Value is the (Sum) of fields..."), and then enter this as the custom validation script to avoid displaying the zero value:

if (event.value==0) event.value="";