Handheld augmented reality (AR) is a unique medium that can be helpful for young children's entertainment and education, but to achieve the benefits of this technology, experiences need to be appropriately designed for young children's developing skills. In the current research, we are interested in identifying and quantifying the usability problems that are encountered by children using handheld AR applications. We have developed a qualitative coding scheme for detecting AR usability problems from video observations of user interactions. We then applied the coding scheme to extract usability problems encountered by children aged 5-10 years old as they played with a handheld AR game. Through triangulation with performance data, we have detected usability problems related to AR and non-AR components of the experience. Our analysis found positive and negative correlations between usability problems and child age, and found that children experienced a variety of problems such as grip and posture strains, inabilities to recover from various types of tracking loss, difficulties orienting their body around the gameboard, etc. This work is the first in a series of studies applying the qualitative coding for understanding young children's ability to use handheld AR applications.