HC-110 and Rodinal have terrific shelf lives, even after being opened. A year-old bottle should not be a problem, unless it has been stored very poorly. Generally, liquid chwmicals discolor as they go bad, but Rodinal may be dark to begin with. Powdered chemicals usually last a very long time in their original, sealed containers. Most will still be good after 10 years. If the material is badly caked or discolored, it is probably bad, however.
When a developer goes bad, it usually just doesn't work as intended. Negatives or prints will usually be underdeveloped or not developed at all. Stains may also appear.