If you'll be in this hobby, you're going to need a good soldering device. Although it doesn't need to be a metcal.
No one thinks they need a Metcal until they try one.

Here's a post I came across on a newsgroup a while ago which sums it up pretty well:
I couldn't agree more. Metcal irons are miraculous. If you haven't tried
one, you haven't been enjoying soldering. It took me months to talk my
new employer into trying one. In less time than that, we now have them all
over the company.
One assembler called it a 'dream iron'. Yes, they're
*that* good. Those of you who work with your soldering station switched on
most or all of the day really owe it to yourselves to try one. They're
expensive, but well worth the money if you solder a good deal. For fine
pitch work, they're not merely a luxury -- once you try one you'll be hooked.
I finally got a Metcal of my own, the same model I used to use when I worked at the PCB factory.
Anyway, Spyridon, did you get your soldering sorted out? As others pointed out, you had some goose-pooping going on there. A low wattage iron combined with being new to soldering tends to give results like that. You want your through-hole fillets to be shiny and smooth, and be shaped like a Hershey's Kiss. Heat the pad and post from one side by pressing your iron down against both simultaneously, and then feed the solder wire (use flux core 60/40, or better yet, 63/37; ~.025" diameter works well for most PCB soldering) in from the other side, pressing it into the pad and post in a steady motion (not into the iron; the heated pad and post will melt the solder); then pull the iron and solder wire away at the same time when you have enough solder in there.
Also, until ThisOldGame gets the authentic style of coin door plates made, have you thought about applying the ArcadeShop sticker to the top of the original plate, and then installing the plate with original-style rivets to the coin door? That would at least retain the look of an actual riveted metal plate rather than just a sticker.