Nobody has offered the advice to dip the wheels (fully inflated) in water, such as a bathtub or kiddie pool, to check for a slow leak. Sometimes the valve cores of Schrader valves (the kind that look like those on an auto) leak because they're not screwed in tight enough. So you should check the valves too -- but that can be done with spittle.
You may be able to get tires with kevlar belts built-in -- dunno much about 24 inchers though -- and those will help prevent goathead flats, in my experience. The problem with tires is that light weight and flat-resistance are pretty much mutually exclusive.