First, an answer to the original question - I see the same behaviour all the time flying a C172 in the rain. As Orionsbelt described, the basic 172 has only single static port, and it is susceptible to water droplets running across it. If you see flicks to +/- 200 fpm and the altimeter jumps up or down 100 feet without there being a corresponding physical "bump", that is what you are seeing.
Answer to the second question, you should log all the time that you fly by reference to the instruments, regardless of the flight conditions. If you are IFR in controlled airspace, even if it is a CAVOK day, you should generally be flying on the instruments because your "VFR" skills and altitude/heading keeping will probably not be to IFR standards. Hence, broadly speaking if you were flying IFR, log it as instrument time.