Other than possible addiction are there any downfalls to benzodiapens for stress and anxiety?

Addiction=main issue. Addiction and related issues (tolerance, withdrawal) are the main concern. Other concerns include possible sedation, dangerous interaction with alcohol (increasing intoxication), impaired driving, some memory impairment, and the risk of seizure if high sustained doses are stopped abruptly. Generally, though, benzos are fairly safe if used rarely, briefly, and sensibly.
Great question. Benzos are "disinhibiting". Even at low dose, intermittent use, you will give in more to your whims. You'll have that extra piece of cake, or take extra meds of other types. You might decide to blow off work. There may be dysfunction in other realms. Also, even when used per iinstructions, there may be withdrawal between doses that worsens and perpetuates the anxiety for which you took it.
Sources of problem. Good idea to figure out sources of stress/anxiety--benzos can interfere with registration coordination alertness--if used correctly are safe ; helpful.