Mine are also turning brown, but mine has been flowering for a while now. I'm going to pull mine out in a week or two to free up some space (in a very large container).

Marginal necrosis and/or browning at the tips of leaves on growing plants without visible pest infestation are usually signs of wet feet, emerging root damage and rot, or blight due to excessive moisture than needed by the roots or insufficient soil drainage and aeration. Tubers also become deformed in heavy poorly darined soil.

Generally, if a plant is overpotted (too large of a planter with respect to the size of the root ball), the plant is also more at risk for root damage and rot and other fungal diseases. In-ground planting is usually 18" apart b/t plants, so it would be less in a container or as directed.

Potatoes need sandy, fast draining soil and be planted in a sunny location.

If blight or rot is corrected early by improving soil drainage and increasing soil aeration either by watering less or repot and amend the potting soil with perlite (the better choice), an affected but growing plant most likely will recover.

Thanks you guys. I think I'll try to reduce watering for a bit and see if things improve. Since it's so close to time to be harvesting them, I think I'll just leave them in their same container and soil. After this batch, I'm already planning on planting another "crop". Hopefully that one will go better. Thank you again.