Some even closer up pictures of the solder joints on the pots would be even more useful.
Being that you are new to soldering or have not developed a lot of expertise, some of the characteristics that you are experiencing may be attributable to the solder joints.
From my experience, I like to use soldering "flux". It comes in a little tub and is cheap. You get it at hardware stores. I get my solder exclusively at Radio Shack because they are the only place I can find that has "electrical solder" that contains "lead". This solder can be purchased at Radio Shack in rolls of thin solder wire - like 1mm or less in diameter. It is easy to work with and melts at much lower temperatures than "lead free" solder. You should "not" use "plumbers solder", all of which is lead free. Use electrical solder.
Get a small pencil type soldering iron, approx. 15 watts, and get a decent brand such as Weller, avoiding store brands. I also have a pencil type Weller soldering iron that is 40 watts, but it gets real hot fast and requires more skill to use and to know when to use it. Don't use a "soldering gun"; save it for other soldering jobs, whatever they may be. A pencil type soldering iron is inexpensive and can be purchased at a "True Value" hardware store or equivalent. Don't forget the flux; don't rely on "flux core" solder. Completely "forget" plumbers solder for electrical applications - go to Radio Shack and avoid a wild goose chase.
Prepare your solder site, on top of the pot or where ever, by applying some "paste flux" and heat it with the soldering iron. You will see it start to smoke - this burns off any oils and impurities and prepares the soldering site. When you use the flux to prepare the soldering site you will immediately notice that when you heat the site of where you are going to join parts, that the solder will quickly melt and "sheet out" at the soldering site - the solder will not "ball up" and roll off.
You want the solder to "sheet out". You do not want it to ball up and roll off, as you will learn quite quickly. Flux is the trick to get the solder to sheet out and adhere well to the parts.
You want to use the "minimum" amount of solder necessary to solidly join the parts, wires, etc., together. You do not want to "pile up" the solder on top of the wires and soldering site. Piled up solder is an easy to spot sign that the particular soldering joint is a "bad solder joint", or even a "cold solder joint". Obviously you want to have good solder joints.
I would unsolder all of my weak looking, piled up, soldering joints and start over using paste flux to clean the soldering site. You can actually apply the flux and wait to heat it up until you have assembled your wires, etc., at the soldering site, and heat everything up at the same time - melting the flux, burning off any impurities, and melting the solder into the soldering joint. I advise using as little heat as needed to get the job done.
Position the soldering iron across from or underneath the soldering site and apply the heat there in such a way that the solder will be drawn across the top of the pot, thru the wires, etc., toward the soldering iron. This way the solder saturates the wire strands and the whole soldering site, rather than piling up on top of the items that you want to solder. Solder is "drawn" toward the hot soldering iron tip, almost like a magnet.
It gets easy with a little practice. Others may advise you to use differing soldering techniques. This is just the way that I like to go about doing my soldering.
Before doing it over and fixing the solder joints I'd make sure to have these items on hand, minimum:
* A good quality "pencil" type soldering iron of approx. 15 watts like a Weber.
* A small tub of "paste flux" and the optional tiny flux brush. Together these cost about 2 - 3 dollars but are priceless.
* A small roll of 1mm diameter or less "lead containing" electrical solder from Radio Shack.
* A yellow sponge with that green scouring layer, cut in quarters, wetted and squeezed out, for wiping off the soldering tip. You want to keep it clean and free of oxidized black material. Keep it coated with a thin silver coat of solder.
* Needle nose pliers for holding hot wires, parts, etc., while soldering. You can use the needle nose pliers to push down on wires to hold them in place as well as to grab them.
Using these inexpensive tools and accessories you will be able to do remarkable things with a simple soldering iron and solder. You will be able to quickly build a body of expertise and be relatively good at soldering. Developing soldering skills will enable you to fix and modify a lot of your guitars, present and future.
So, without insulting you, it is obvious from the pictures that your soldering joints need some work. I can tell this because the solder does not show any evidence of "sheeting out", and I see where it is piling up. Less than ideal solder joints, as in the ones shown in your pictures, can be the source of a lot of problems that show up when concluding the job and testing the guitar when finished. You want to pay particular attention to having good solder joints at all "ground" points, such as on top of the pots and elsewhere.
Also, check your work and look for wires that pull off with almost zero force, and wires that may be touching each other (bare wires). Double check your wiring diagrams and don't be afraid to ask for guidance when it comes to your wiring scheme.
It is super easy to wind up with a malfunctioning wiring job and double and triple checking things can lead to you discovering where things went wrong. Often a bad solder joint will be to blame, and from just looking at it, it might look like it is an adequate joint - but after you unsolder it and do it again more carefully you may frequently find that the funky looking solder joint was the problem area after all.
Knowing how to solder is a great skill and will help you solve lots of problems, as well as make upgrading to nicer pickups, etc., much more inexpensive. Don't let yourself be intimidated because it is easy to develop excellent soldering skills with just a little work and attention to detail. Get the right stuff and you will be "way" ahead of the game.
I hope that you find my sharing of my own personal experience to be of use to you in your own quest to learn how to do most all of your own soldering. Your soldering work is definitely an example of a "good try", but you may need to go back and do some of it over and work on developing your soldering skills.
Good luck and that is a very cool looking guitar. I hope you or others find what I have shared about my soldering experience to be useful. When I was a child of six or seven I was fascinated by the tools in my dad's work shop. I particularly liked soldering and repeatedly burned my fingers and hands on the soldering iron and more than once was shocked by drops of liquid melted solder dropping on my skin. It didn't take long before I started learning how to practice soldering safety, with and without success.