I have had a False Shamrock (Oxalis triangularis) planted in a clear, fishbowl-like container with a handful of gravel for drainage and potting soil to the level of the pot it came in for about a year now. Recently, I have noticed green, algae-like blooms appearing and they have now covered the inside of the pot on the side that faces the window (I have just rotated it so they no longer do).
Will these cause any damage to the plant and its roots, and if so, how can I get rid of these?
Unfortunately, its the light that causes the algal growth. Now you've turned it, the other side will produce algae in response to the light - the brighter the light, the stronger the algal growth, just like an aquarium or fish tank, and it may eventually turn black. One of the disadvantages of planting in clear containers I'm afraid. I agree it shouldn't harm the plant, although excessive growth will be pretty unsightly, and you may get excessive growth since your container seems not to have drainage holes.
The algae shouldn't hurt the plant, but if you are seeing a lot of it, you could be over-watering, which can hurt a plant... people will say that the algae will compete for nutrients, which might be true, but it isn't on a scale that you would expect to be able to observe.
