The corn plant looks pretty good. They are sensitive to chemicals in tap water, so it's normal for the foliage to have some imperfections if the water has fluoride, chlorination, &/or lime. Distilled water, rain, or condensate from a dehumidifier or A/C can be used to avoid issues from those chemicals. If not possible, advise taking the plant to shower or outside in the shade to water so the excess can flow out of the pot. This still exposes the plant to some of the chemicals but at least prevents a build-up of substances in the soil.
When you remove the old pot, you'll probably find a pancake of roots at the bottom. Cutting that off will allow the roots to be able to grow normally again for a while, and make removing the old soil much easier. Looks like it could use a bigger pot if possible. That would help it be able to stand upright. 3-4 softball/cantaloupe sized rocks around the base after repotting might hopefully eliminate the need for the stake. Hopefully the trunk isn't actually wobbly without it. Rotating it halfway every week or 2 should help keep it going straight up.
Edited to add... those rocks will be heavy. Once the roots get situated into the new soil, hopefully they won't need to stay. Watering with a gentle sprinkle the first few times will prevent unnecessarily compacting the soil, as a more forceful gush of water would. I'd probably water lightly (slowly, and not adding enough so that it comes out of the drain holes,) as needed without moving the plant for the first couple months, then try removing the rocks, if they were needed at all, so it can be carried somewhere to do a first thorough watering, but still with a slow, gentle sprinkle, using enough water so that some water does come out of the drain holes.
