I can see a couple of problems with what you've posted up about your fish. Unless your 0.5 gallon tank is temporary, I would strongly suggest upgrading to at least a 1.5 - 2.0 gallon tank for the benefit of both you and your fish.
Tanks under a gallon are difficult to maintain, as you would be doing daily water changes to keep the water parameters stable. Ammonia and nitrite levels would need to be closely monitored because even trace amounts such as 0.25ppm, are enough to cause a whole slew of problems - everything from listless behaviour, to burning around the gill and fin areas.
You mentioned that the water is kept at around 70 degrees. This is much too cold, and is probably resulting in your fish's lack of appetite and lethargy. The problem with tanks under a gallon, is that there is no real way to maintain a consistent temperature. Usually the only heaters available, are those that raise the temperature of the water a few degrees above ambient room temperature. However, constant fluctuations of even only a few degrees can severely compromise the immune system of your fish, and definitely won't help if there is an underlying health cause for his behaviour.
Finally, if you have your bamboo completely submerged, it will eventually rot and pollute your water. I believe it is supposed to have only its lower stem submerged, with the water level kept below the first leaf node.
If this was my fish, I would firstly invest in a minimum 1.5 gallon tank and a suitable heater (preferably adjustable and with an inbuilt thermostat). I would perform 50%-70% water changes every second day, and would transfer my fish onto a diet of a good quality pellet food as well as the occasional offering of something high-protein like frozen brine shrimp or bloodworms.
Imagine if you were being kept in such a small body of water with nothing to occupy your time but some gravel and a single bamboo plant. You would undoubtedly be very bored, and spend most of your time moping. Filling the tank with betta-friendly and idiot-proof plants such as anubias and java fern, will give him a territory to explore and patrol and something to do. You can also provide outside stimulation by putting the tank in a high-traffic area so that there is always something different going on to catch his attention.
The fuzzy spot could have been anything from a mild fungal infection to a case of columnaris. Nine times out of ten, poor water conditions are to blame for health problems in fish. Proper care and pristine water, should ensure that you have a long time to enjoy your new fish.