Annoying frames in final render After Effects.

If the edges of your layer are not perfectly aligned to the pixel grid they will be antialiased.  I am assuming that layers 13 and 14 are causing the problem and that they are scaled and repositioned. You have applied Screen and Add blend modes to those layers so if the edge of the frame on either of those layers is not 100% black you are going to get gray edges when they are anti-aliased. The easiest fix is to apply curves to those layers and drag the black point to the right a little. To preserve the look you could select the Rectangular Tool, double-click the layer to add a layer sized mask to the layer, change the mask to subtract, shrink the mask a few pixels using a minus value for the mask, then set the compositing options for curves to use the mask. Here's an extreme example of that. A poorly created gradient filled shape with a bad edge that is exaggerated so you can clearly see the problem, a mask applied, curves applied and the compositing options set to use the mask so the Curves Effect turn the gray edges black and the composite is now fixed. The Before and After Comps are identical except for the Mask.

In the future, select the layer that is giving you problems, press the 'u' key twice to reveal all the modified properties, and we can be sure that we give you the right advice. I'm pretty sure that it's nothing more than edges that are not black because the layers were scaled and repositioned or because you added some color correction that fouled up the edges.

Another possible fix is to just pre-compose the overlay layers with the blend mode set to normal, then apply the blend mode to the pre-comp. 

Let me know if it work - if not - maybe something else will help. 

It hard to say without knowing exactly how your project was set. But for me it looks as borders of layer with your explosion that was keyed out fro background - if that is the case simle Garbage matte (masking out borders should help.