Our system does this and I think its a bad Idea (for us any way), our target market is UK and Ireland. But when google was crawling our pages they were only getting the US version of the site, so all that nice text we had for the UK and Ireland pages was was missed by google (the US page was the systems default page, with no custom text). I just copied and pasted our UK & Ireland text to the US default page, then we started to rank for some of the targeted keywords.
Now our problem is that is google bot is getting the prices us dollers instead of Pounds or Euros so for some of our rankings it picking up meta data and showing $ prices in the serps for the UK.
So my advice is be careful, it might seem like a good idea for users, but google will only see the US version of the site
To answer you questions:
- How will Google index these pages? Will it index the www.mywebsite.com (Japan version) in its Asia archives and the www.mywebsite.com (US version) in its North American archives?
It will only index US version for all
- Will Google penalise us for showing different content across Geo-locations on the same URL?
To my knowledge no (we used they system for 3 years and rank modestly)
- What if a URL is meant to show content only in Japan?
Not sure what you mean, but you need different urls for different content
- Are there any other issues that we should be looking out for?
See what I said above