How dangerous are rescue drugs for asthma?

Safe. Albuterol and the other rescue beta-agonists are generally safe. You may get a rapid heart beat ... But it is better than dying of asthma or suffering. The reason we like to minimize rescue inhalers is that they don't treat the underlying illness - airway inflammation. Inhaled steroids do this well for most sufferers. See your doc for more information.
Relatively safe, but. The short-acting beta agonists (albuterol) do have some side effects like palpitations, etc.But are relatively safe. The long-acting beta agonists (laba) are recommended (alone) in COPD but not asthma. There have been links with severe side effects when labas are used without steroids. In the us laba are often available in combo with steorids and used as a controller-not rescue.
Not dangerous at all. Rescue medications like albuterol are analogs of Epinephrine & norepinephrine, 2 chemical hormones made by your body that have multiple effects stimulating lungs, heart, muscles & gut. Rescue drugs are chemically designed to have little effect on any organ other than the lungs. Overuse of rescue drugs may not be sufficient to control asthma. When use exceeds 2x/week you also need controller meds.