I haven't had any of my own animals on thyroid medication, but I work in a vet clinic and I have seen many animals who use thyroid medication over a period of time. My experience has been that as long as the owner gives the drugs as prescribed and keeps a close eye on their pet at least until the drug is being maintained at a therapeutic level, it's easy to spot complications before they become a problem.

Periodic blood testing once therapeutic levels have been achieved helps the doctor keep track of any long-term effects the drug might be having, although I must have missed the horror stories your friend has heard, all I've heard of are very occasional and not terribly severe immediate reactions to the drug, the drug not alleviating signs of hypothyroidism, or reactions because the dog got an overdose.