Nice work, @Jeehroen. I see lots of cold solder joints, though. I guess you have to rework about 90% of them and until then it's probably hopeless to search for single points of trouble.
I see many pins barely wetted with solder, much less with a connection to the copper track. Putting a blob of solder onto the tip of the wire is fruitless. The solder has to melt into the copper. It has to flow 2 or 3 millimetres on it. This takes at least 2 seconds, sometimes 4 or 5, there's no hurry to remove the soldering iron. Also, isolation milled boards like yours take a bit longer for each solder point than the etched ones with thin tracks.
In case it doesn't work satisfying on the first try, suck away the solder with a sucking pump or solder wick, wait a moment for cooling, re-clean the iron tip and try again. You can try as often as you want.
Another one is, leaded solder is much easier for beginners than lead-free one.
Ideally you'd find someone showing you how to do it. It isn't difficult once you found the "trick". Until then, here are a number of soldering tutorials: [
makezine.com] , especially this one: [
www.instructables.com]
BTW., the joints of the ATX24 header look mostly good!