How about a metal edge. With a bright colored laminate it screams 50's diner retro style. (which is too cool btw) but I don't think it would look that way with yours, just more modern. It could be a nice easy inexpensive solution that's probably better then the sharpie pen huh? :)

I wouldn't do a metal edge, to me they look very 1960's. I'd get a file and very gently file the roughness smooth, then use the sharpie to color it. You probably won't even notice it once the sharpie colors it.

Use a Sharpie, or have a professional fabricator redo it.

I don't find metal edges 60s style at all.

From tilelines.com metal edge

And IKEA

They do look good! Except for the edge. I was gonna say to use a Sharpie.

I have that Formica laminate in walnut (dark brown). My counter is rounded at the front, but I had the same problem at the squared sides and seam. A brown Sharpie worked just fine.

I think they also have paint pens at the craft store. That might also work.

We have installed laminate over our existing countertop, and the edges look perfect. It sounds a bit like the edges were not cut and sanded properly. Or maybe the tools that your dad used to cut the edges were not the right ones, or were not sharp enough so the laminate ended up rough.

We used a router to cut the excess off at the edge and its important that the router bit is the one used for laminate trim - a flush cut bit. Also, presumably the router bit should be sharp, not old and rough. We also then took a sanding file so that the edge wasn't too sharp. Ours looks great.

If the Sharpie by itself doesn't do the trick, could you use a file to smoothen out the roughness? If nothing works, perhaps try again by installing another piece of laminate. There are lots of youtube videos that describe the process. I think that is how we learned how to do it.

Nosoccer mom's photo of the metal edge does look good, a contemporary look if that is what you are going for. I was thinking of the old style metal edge, which our first house had (built 1963) But, if you prefer the formica edge, then I think the filing/sharpie should take care of it pretty well. Daylily is right though, it looks like the routering was not done as well as it could have been. Still, I'd give the filing and sharpie a try first, if that doesn't work, you can always add the metal edge, or another laminate edge as daylily suggested. Good luck.

It looks like a lot of the roughness is nubs or residual contact cement. If that is the case, you can remove it with a rag wetted down with lacquer thinner. Follow up with a laminate file if it's still rough and the color with a Sharpie as others have suggested.

Otherwise, you might want to run a router with a fresh new laminate flush or bevel trim bit along the edges. It's possible that the original bit or bearing was gummed up with contact cement and didn't trim as flush as it should have.