Thanks to everyone who contributed to this thread. I spent a lot of time reading and then took action - just a few days ago. My XFactor Style Made for Adsense site that I used for testing this out, had lost rankings on 6/2 and even with lots more links I was not able to make it back to page 1 within Big G. I was stuck on page #2.
I moved the site from plain html files to Wordpress (and for now removed Adsense). Since the overall site was kind of shopping related, but not really, I took the advice from this thread and added the "shopping signals". For one I had checked the competition that was on page 1 ranking for my main keyword (which is also part of the domain name). They all had shopping related websites with shopping cart, buy now buttons, product descriptions, and product prices. None of the sites on page #1 was informational in type. So, I updated my 300 word articles with more shopping related content and more shopping related factors. Well positioned pieces of product description, buy buttons and stuff like that. I guess it also did not hurt t add more links, too. I made sure every tag and title got updated to meet the shopping category.
Today I am #6 on page #1
I am not sure if this based on the findings here, but it matches several things. The main keyword shows the shopping category in Google (left column), but my old site only had some short articles per page and was more a review or informational site. I hope by adding the Google category related stuff that it helped to move the site backup again and to have it recategorized.
I had removed Adsense and will wait a few more days before adding it back. I also had a lot of Amazon affiliate sales before (before March 8th), but I have to use some Google Affiliate Network merchants now since Amazon no longer allows people from Colorado in their affiliate program. Needless to say that no online shopping site converts as good as Amazon does - I had 1 single conversion from other merchants for this product (and I tried buy.com, Walmart.com, Target.com, and some smaller ones).

At least I hope to make an occasional affiliate sale now maybe, but I really hope that my Adsense income for this site partially picks up again. With 6/2 it went down from $200 a month to $1.67 for the month of August.
Anyway, I hope this gives a little bit back to everyone here. As it looks right now, this thread has really opened my eyes of what happened with the Mayday update.
I will work on other sites of mine that suffered now the same way to see if I can reproduce these findings. Thanks, again - especially to Mister Gemini!!!!!!