These are two slightly different cases:
1) With Tiled Backgrounds and fractional rendering and linear sampling, the opposite edge of the image can wrap around to a transparent edge, creating a seam. Adding a line of transparency along the opaque edge of the image usually fixes this.
2) With images rendered from spritesheets which are downscaled a lot, there can be bleed from the mipmap. This is an inherent problem with any tool that uses spritesheets and mipmaps: the smaller the mipmap, the more content tends to bleed in to other images. Think of the 2x2px mipmap, where essentially each entire quarter of the spritesheet has become a single color, representing a combination of all the images in that entire quarter of the spritesheet. That happens but to a lesser extent with higher mipmap levels. This is why Construct lets you choose high quality downscaling mode: it pads every image on the spritesheet to a power-of-two size, ensuring it can be resized much smaller before any mipmap bleed happens - but comes at the cost of increasing the memory usage, as all images have to be padded.