ah right, yeah if it's a 2nd hand alternator then it could be knackered. Best way to test, start engine, turn head lights on, wipers on, rear screen demister on etc...etc... then put a multimeter across the battery terminals, if it reads less than 13.4volts then your alternator isn't doing it's job.
So is the only problem you are having that the battery light stays on sometimes? Mine has always done that, never caused any other problems. Although maybe your idle speed is slightly too low?