Let's say you have an expression set to x / y, where y has the potential to be zero. As you experienced, SSRS will change this value to #ERR (or sometimes NaN).
Your first instinct would be to test for zero
=Iif(y = 0, 0, x/y)
Unfortunately, this can result in a debugger warning that says you are attempting to divide by zero. This is because SSRS attempts to evaluate the entire statement during compilation.
As a result, we need to provide SSRS with a value that it can evaluate
=x * y ^ -1
This is the same as dividing by your y value, but SSRS sees this as dividing by infinity, and therefore can make an evaluation.
As a final step, you will want to make sure your code can properly export to Excel. Under 2012 SSRS (and possibly later, I haven't tested), SSRS has an issue where possible zero values export to Excel as 0.000000000000000 and cause loss of data errors.
To correct this, we explicitly output the value of zero
=Iif(x = 0 OR y = 0, 0, x * y ^ -1)