Should Japan be punished for their lack of actions with Fukishima?

I don't think punishment is what is needed here. How are you going to punish Japan? I mean seriously, give them a huge fine? And no I am not trying to be funny.
Japan had a very fast reaction time considering all that was going on due to the earthquake and tsunami hitting them all in an extremely short period of time, dealing with massive death and destruction.
And not to sound like an ass but I would keep a media blackout in place because most media is very irresponsible in their reporting because they need sensational headlines to sell their stories and sadly facts don't sell headlines as much as hyped up tidbits do.

missed spelled Fukishama in the post title. Yes they should, the actions of all Nations can and do have a profound effect on the global climate.

Punished how?
I hardly think the Japanese purposefully spread radiation all over the Pacific, after all the last time they did that, they got Godzilla stomping through Tokyo.
In all seriousness, some bad decisions were made. But they had just suffered a massive earthquake, a Tsunami, and problems in multiple reactors simultaneously. We can Monday-morning quarterback this, but in truth they were simply overwhelmed beyond their ability to cope.
The best thing the Japanese (and other countries who rely on nuclear power and had accidents, as pointed out by CPT L S) can do is ensure that their facilities are prepared to deal with natural or human-error caused disasters, security measures and emergency drills are well-rehearsed, and nuclear facilities are sited properly.