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The site in your profile, for example, has a homepage with many ill-constructed HTML tags, and it's definitely worth checking out the site you've written - at best, poor HTML makes no difference; at worst, it'll confuse a web-bot into missing links into the site.
My most recent experience with Googlebot is a site I set up in the end of May. Google indexed my home page within a week of submitting it.
Two weeks later it came back and grabbed the home page again.
One week later it grabbed about half the site. Then began to index my home page daily. (Just before the June update)
One month later it took in the entire site. (Just before the July Update)
Some of Googlebot's activities are driven by timing. For example, googlebot is very active just before an update. This entire website was crawled heavily the past two days (all 250 pages). I suspect google is attempting to grab fresh content before an update that should occur in the next 7 - 14 days.
This is about the 10th website that I have launched and from my experience creating a more dynamic home page seemed to help. Since it changes daily I think Googlebot found it more interesting.
I don't think adding Adsense will help with indexing. You might want to try making the home page less static.