>>2209061Magic wand tool, man. You can mark off big swaths of not-quite-properly-gradient and make them gradients like that pretty fast.
As for cleanup, there's no such thing as a 'correct' way, only tools and methods that get you closer to a clean image. it's whatever gives you the best result. I work in digital design, and even amongst professionals, we've got plenty of variation in tool usage for the exact same tasks. Experiment, experiment, experiment. If someone here posts a particularly interesting cleanup job and you're interested, just ask them for their methodology politely and I'm sure they'll let you know.
Regarding some of those botched areas, especially around the embroidered typography on the hoodies, don't be afraid to bust out a good old brush tool like the mixer brush to smooth out bad transitions or color bleed. See vid for super quick example. Remember that a solution doesn't *have* to be complicated.