"I think there's an overwhelming belief now that China, at the very least, doesn't respond to cooperative behavior. What can be said is that China behaves the way it does regardless of whether Japanese behavior is positive or combative," Lee said.
Then there's the question of how Japan powers itself amid the backlash against nuclear energy following the meltdown of the tsunami-hit nuclear reactors in Fukushima.
The LDP has called for safety tests on all nuclear plants over the next three years. Those that pass should be brought back online, Abe has said.
He'll also have to deal with the enduring task of cleaning up communities shattered by the earthquake and tsunami in 2011, and contend with local anger that the recovery seems to have stalled.
Despite all the challenges, some analysts remain optimistic about Abe's ability to put Japan back on track.
"Japan has never looked better to me. I'm very, very optimistic on it," said Ben Collett, head of Japanese equities at Louis Capital Markets in Hong Kong.
"I'm hopeful for the market and the economy and Abe's timing is solid. He'll initiate a cycle of new industrial development -- a rebirth of heavy industry in Japan that includes energy, hi-tech, space exploration and defense industries."
Henry says it should be "fairly smooth sailing" for Abe for next one or even two years if he watches his words on three key areas.
"He's got to be careful what he says about BOJ policy, he's got to be careful geopolitically about how he approaches Japan's "friends" and competitors in the Asia region, and he also has to be careful about putting his own Cabinet together to make sure that a week or two into his Cabinet we don't have any resignations because somebody has done something."