My Haworthia started to have brown spots on its "leaves" after a month of owning it. It doesn't look too bad but I want to make sure it's not dying. My room only has a north facing window so that's where it gets its sunlight from, and I try to only water it once a month.
Those brown spots are dead patches in the skin. Not from lack of water. That's most commonly seen when a plant is brought from a low light area and gets some direct sunlight. It's not really going to hurt the plant in the long run, based on your picture, but it is unsightly.
Also, you're plant is etiolated. Not enough light. See in the center, where the new growth is thin and yellow? Be careful though if you move it to a brighter spot, because even though the plant needs more light, it isn't accustomed to it, and high light levels will damage the leaves again.
PS: I'd water based on the moisture content of the mix, rather than monthly. I'd water whenever the mix dries out more than 1-2" down, during the summer, and then just enough over the winter to keep it from drying out completely.