Forget Me Nots aren't really a pond / bog plant, but rather a woods / meadow plant. They like partial shade and moist, but not soaking wet soil. I have them in my front garden. They're self-seeding and as such they migrate from year to year. If they're growing on the margin of your pond, I'd not worry about them too much. The leaves below the water line are browning because it's not an aquatic plant. They actually like water , but in a well drained soil (damp soil as in shaded forest). They don't like being water-logged. They're an annual and grow where seeds are dropped. If you aren't careful, they can actually get a little out of hand, I have them growing in my front lawn, but they were originally planted in my front garden.
Don't worry about browning leaves as they are just too wet. As long as the roots of the plant aren't saturated, they'll do fine. I have mostly blue ones, but some have mutated I guess or have been cross pollinated, so some of the plants are producing white or very pale purpley-blue flowers. Ones growing where you don't want them next year, just pull them up like you would a weed, or mow them over. Hope that helped a bit. None-the-less, a very lovely plant to have. Very low maintenance.
BTW.... the wiki article says they flower mainly in the spring, but I beg to differ .... you'll have flowers during much of the spring and well into the summer depending on when the seeds germinate. I've had flowering plants well into August.
A bit more info >
http://en.wikipedia....i/Forget-me-not