The criminal rating is accumulative. For each crime you commit and for each incident where you cause mass destruction and/or mayhem, the criminal rating will rise. However, using certain cheats (namely the weapons and/or car spawning cheats) will reduce (and sometimes, even temporarily freeze) your criminal rating. The criminal rating is just for statistical purposes, it has no impact on gameplay, other than saying how big of a cheater you are.
The Media Attention varies based on how much media attention you are getting. Basically the longer you stay on 6 wanted stars and cause mass destruction and mayhem it will go up. It will gradually decrease if you don't keep this up. Unlike the criminal rating, it doesn't decrease. However, similar to the criminal rating, it has no impact on gameplay, other than saying how much of an attention magnet you are.