Here are links to a couple of posts about Transient Lunar Phenomena on the other blog.
The first type, which last less than a few seconds and are not controversial involve the effect of meteors (meteorites) impacts on the moon. It is not unheard of, especially if you have a decent sized telescope and lots of time or a continuous CCD recording to occasionally see very tiny flashes of light on the unlit parts of the moon. Over a period of many years and hundreds of hours of observation with a 8-inch aperture telescope, I have seen a few tiny flashes, especially when looking at the lunar terminator.
TLPs, in my opinion, are likely due to the release of gaseous compounds (containing sulfur and nitrogen) and basaltic dust by volcanic features similar to Fumaroles and Fissure Vents on Earth. Their distribution on the moon might be linked to the presence of thin and fractured lunar crust. Of course, accepting such an explanation would mean that much of what we currently believe about the internal structure of moon and other celestial bodies of similar sizes is rather incomplete.