Inflate the air mattress. Wait to see if the mattress looses air on its own. Listen for any sounds of air seeping out of the mattress. Lay on the mattress and listen if you're having trouble hearing anything.
Inspect the mattress for holes. Holes typically form on the bottom and sides of mattress. Check the seams closely because this is where factory defects are likely to appear.
Run your hand over the air mattress slowly to feel for possible air loss.
Rub a sponge with soapy water around the mattress's edges and inflation valve. Watch for bubbles. Work in small sections for less of a mess. Dry each section before moving on to another section.