The Gemini Planet Imager (GPI) has excelled in imaging debris disks in the near-infrared. The GPI Exoplanet Survey imaged 24 debris disks in polarized H-band light, while other programs observed half of these disks in polarized J and/or K1 bands. Using these data, we present a uniform analysis of the morphology of each disk to find asymmetries suggestive of perturbations, particularly those due to planet–disk interactions. The multiwavelength surface brightness, disk color, and geometry permit the identification of any asymmetries such as warps or disk offsets from the central star. We find that 19 of the disks in this sample exhibit asymmetries in surface brightness, disk color, disk geometry, or a combination of the three, suggesting that for this sample, perturbations, as seen in scattered light, are common. The relationship between these perturbations and potential planets in the system is discussed. We also explore correlations among stellar temperatures, ages, disk properties, and observed perturbations. We find significant trends between the vertical aspect ratio and the stellar temperature, disk radial extent, and the dust grain size distribution power law, q. We also confirm a trend between the disk color and stellar effective temperature, where the disk becomes increasingly red/neutral with increasing temperature. Such results have important implications for the evolution of debris disk systems around stars of various spectral types.