The gaps are between tiles, not within tiles. I see what you are saying if the gap is within the tile.
I think the problem is related to the cell size. The images are supposed to be 4" resolution and the cell size says 0.33 ft. The extents also seem to have precision down to 0.01 ft. The leftmost column of images start at an even coordinate. I think at some point the 1/300 (0.00333...) ft that is missing caused a pixel not to show up. The coordinates in the extents will run like 0.66, 0.32, 0.98, 0.64, 0.30, 0.96, ... .
I am just wondering if there is a way to make the mosaic dataset sample from the pixels that are around the missing row and display the data in the final mosaic.