Home made trailers are a hit or miss proposition. Done right they can be better then a manufactured trailer. Done wrong and you have a nightmare on your hands.
Things to look for:
-Metal is to light, frame is the biggest worry point here.
-Welds are bad. Some of this could be visible as in cracks but you might not be able to tell if there is poor penetration. Also, if the metal is not prepped proberly there could be contaminated welds.
-Axles not properly aligned, this you can check by looking at tire wear and see how it pulls. This can also be an issue on manufactured trailers but generally attributed to bent axles.
-New paint? Might be hiding metal that was not prepped properly to begin with.
-Bad wiring. Connectors not crimped properly or loom not properly protected from sharp metal which cuts the insulation.
That's just from the top of my head and I'm sure others can add to the list. All and all I personally would stay away from home made trailers unless I knew the person who built it.