See attached photo, I can see the threads on the drive side of my axel. Is this something that I should be worried about?
Edit: Other side for reference
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The two nuts inside the fork should be tightened against each other, as they are in the second photo. The outer nut is normally referred to as a lock-nut, because it's used to lock the other nut in place by being tightened against it.
This is critically important with open bearing systems, as precise adjustment of the cones on open bearings is what makes them work (and stops the balls escaping). With sealed bearings like yours it's less important, as the inner nut on each side effectively lock against each other via the two bearings and the spacer. Viz, there is continuous metal around the axle inside your wheel, so you can do those nuts up nice and tight. Caveat: there should be continuous metal. Obviously the manufacturer can save a few grams by leaving out that spacer, and in that case tightening the nuts properly will destroy the bearings. To find out, check that the axle still rotates freely when the nuts are done up.
The problem in your case is that you have a deep, strong axle nut on the outside of the fork that is done up nice and tight to stop the axle sliding in the dropouts of your single-speed. Unfortunately that big hefty nut is tightening against the skinny little locknut on the other side of the fork, rather than against the locknut plus nut etc assembly. You're likely to damage the locknut and may strip it, which would mean the drive side of your axle would be able to slide, dropping your chain.
You can avoid that if you never do up the outer axle nut very tight, but in my experience that inevitably leads to the axle slipping in the dropout, the rider doing the nut up tighter, and the locknut stripping or deforming.
I am far from an expert in Single speeds. However, It's not right and I would fix it purely for that reason, let alone potential problems. To me at best its a 'broken window'
If the outer nut comes loose the wheel comes loose, axle will shift and gernally bad things will start to happen. If the inner nut comes loose the bearings will come loose and the wheel will wobble. How likely these events are I have no idea. I see nothing preventing the inner nut loosening - thats why the outer is there - as a lock nut. The outer should be OK as its locked against the frame and nut on the opposite side.