Painting process for outside wrought iron

When you say you can see the brush marks, do you mean that they're actually irregularly surfaced? I mean - are we talking just a visual effect or an actual difference in the depth of the paint?

If the latter, do a skim coat with lightweight joint compound and when it dries, either lightly sand OR smooth with a large, slightly damp sponge, then apply primer.

As for your own brush strokes - orient the roller so the roller bar leads your motion. If you're moving right, put the bar on the right. If you're moving left, put the bar on the left. The most pressure will be on the roller bar side, so keeping that side on the "front" of your motion will mean the lighter touch side (the back) will smooth out the uneven strokes as you pass over it again.

Now if its not a real issue with texture, just that your seams are obvious - then just prime it again with a good HEAVY primer, using the proper brush techniques, and you'll be fine. :)

If the prior owner used caulk, and they were really dumb and didn't use paintable latex caulk, then its possible that this would be the result.

Regardless, obviously the paint isn't taking properly here - so yes, the answer here is get a quart of primer go over the edges with a brush, let it dry, and redo the corners.