When you water your plant, do you remove nursery pot from the cache pot?

No I don't, but I make sure that the saucer underneath the plastic nursery pot inside is not full of standing water. IIn fact the saucer is humidity tray, with little pebbles and a tiny amount of water at all times.

The peat in the potting mix could be the problem. It tends to stay too soggy. Usually better to have something faster draining even if you then have to water more frequently.

It does look like there's some buildup of salts/lime scale accumulating on the top of the soil - the white stuff. Certain plants are sensitive to this, and it can be toxic to them. One can avoid this by removing the inner pot for watering, letting it drip out in a sink before putting it back in the cache pot.

Not familiar with Brita filter, does it remove lime? If not, maybe you could collect rain water for your plant. Do you have other plants?

This is a very nice looking Anthurium, BTW!

Thanks for the advice anyone. I don't have rainwater to give it, we had a drought year, but I bought some distilled water for my houseplants to try to curb the salt/lime scale issue. A couple more questions remain....

Should I cut off all the damaged leaves? It wouldn't leave me with very much of the plant left. And I will repot without peat moss, but what is a good mix for the potting medium ? Or just regular old potting soil for this anthurium?

A lot of Anthuriums are epiphytes, so they like air passing around their roots. You'll find that an orchid mix works well for them. Needs to be free draining and light. "regular old potting soil" tends to be too compact and doesn't allow sufficient aeration. At worst is won't allow proper drainage resulting in a build up of stagnant water around the roots..

There's some great potting mix recipes over in container gardening that might work too...
Uncomposted pure peat is such a terrible medium for almost everything, but it used for everything from cacti to aroids...it's pathetic!

Agreed!

Thanks for your replies everyone. After a lot of research I had come to the conclusion that it was most likely one of two things - either sunburn or cercospora leaf spot. I don't think it's the cercospora fungus because the spots are dried up. I think it's actually sunburn, because although the plant sits in a spot where it gets indirect light, I have occasionally set it outside on our balcony to "charge it up" with some light, which in hindsight may have been too harsh. Any thoughts?

Possibly, but sunburn would be more manifested on all of the leaves, not just a couple. What time of day? Between around 11 am and 3 PM especially, the rays are too harsh. Morning is usually best if there's a choice, just because it's cooler then.

This one gets maybe a few minutes of sun in the morning, then from about 4-7. If it couldn't handle that, I'd work it in on the east end of the porch for morning sun instead.

I would strongly encourage you to repot with something that doesn't have so much, if any, peat. This discussion is about a different plant, but the stuff about the clay/plastic or glazed pots and porous, non-water-retentive soil pertains to any potted plant.

With epiphytes, think about how, in nature, this plant would be living in the crook of a tree trunk. Many of the roots would be exposed to air and only moistened during a rain or by dew overnight.

Thanks for your reply, purpleinopp. Your anthurium in the photo is really nice looking. I probably never clarified before now that the majority of the leaves ARE splotched with dry brown patches. The new growth and a couple leaves are still shiny and beautiful, but about 80% of the leaves are damaged to some degree, some a lot worse than others - which is why I was hesitant to cut off all the ones with splotches. I only removed the ones that were really bad, like the close-up leaf photo above. I used to move the plant outside occasionally in the morning for a few hours usually. It was on a west facing patio with an overhang, not getting direct sun on it, but a few times I might have left it out a little too long when afternoon sun started shining down. I won't do that anymore. I have already repotted the plant - I got a new 6" plastic container (same size) but used some Miracle Grow orchid mix. Then today I looked at the Orchid Mix ingredients and peat is a main component. So it looks like I'll need to redo it again. I will also consider planting it in a terracotta pot and saucer insteaD of plastic pot with a cache pot.