Never test for exact equality. 0.1 + 0.2 does not equal 0.3 in binary floating point, because those decimals have no exact binary representation.
Catastrophic cancellation is the dangerous one: subtracting two nearly equal numbers destroys precision. The textbook case is the quadratic formula, where one root must be computed via an algebraically equivalent but numerically stable form.
Summation order matters. Adding many small numbers to a large accumulator loses the small ones; Kahan summation recovers the lost precision by tracking the running error.