It sounds like there was a problem of some kind either with the thread or the stitching. I would just go ahead and re-stitch the seams...maybe using a slightly smaller stitch length.
You can also do a "mock" French seam by just stitching the regular 5/8" seam then folding the edges to the center of the seam and stitching again close to the fold. This serves two purposes, encloses the raw edges and gives another row of stitching. I love this for kids clothes!