Is it safe to give my 10yo with mild asthma albuterol inhaler that expired 1 year ago?

No, because:: It is important that you have constant access to asthma medication for your child, especially in preparation for when a child travels or misplaces an inhaler. If the only available inhaler is one that expired a year ago, you don't know how empty it is or how effective the medication inside is. Speak to your primary care provider asap and obtain new inhalers.

Probably: Pharmacology today states many drugs are still effective after the expiration date ; with the exception of the antibiotic tetracycline. The medication may not be "full strength" any longer, but it should generally be safe for short term use or mild conditions. Severe asthma can be a life threatening medical emergency in a small child. Contact your physician if in doubt.

Maybe: The inhalers slowly leak medicaion so if he isn't improving any with one threatment you need to get a new one.