Not a career but definitely an amazing experience.
Pros
Japan is such an interesting country to live in, everything feels novel and different, and you can really get involved in your local community and culture. The job is relatively easy, the pay for Japan very good, you have lots of time to travel, and you can utilise your free time in what ever means you want so there is a lot of room for "self-development" (e.g. studying Japanese, becoming an avid blogger, getting involved in voluntary work.)
Cons
"Every situation Is Different" is the most apt phrase regarding the JET Programme. You might be put in a city that has lots of foreigners and where lots of Japanese people can speak English, or you might find yourself in the middle of no where where you have to learn to speak Japanese or else become a recluse. Your school might involve you in everything, or they might just make you sit at your desk every day by yourself ignoring you. You might have to lead every lesson and get the opportunity to think of challenging lesson plans, or you might be stuck following the textbook only acting as a human tape recorder. Some aspects of Japanese culture, and especially if you're rural living in an area where there's few other foreigners, can be quite challenging. Though some people do stay in Japan as ALTs or teachers, for the majority of participants this isn't going to be a lasting career and there is no real room for progression in the job.