Sorry for the delay - I just got back from my vacation.
I went ahead and installed a brand new WP 3.5.1 from scratch and activated SREP on it. I then created a bunch of posts with different widgets on them - everything including schools, Yelp, mortgage calc, Neighborhood Profile, charts from Trulia and Altos Research published correctly.
If you haven't requested to raise your API calls quota from Yelp, please do so. 100 calls is very little - Yelp requires to make calls every time a page is loaded (caching is not allowed). A single Yelp table with 6 tabs (Grocery Stores, Restaurants, Banks, Gas Stations, Golf Courses, Hospitals) makes 6 calls to the API at once. If you're working on a page that loads Yelp data and visited that page 5 times - you're already over 1/3rd of your daily quota! So, please, follow Yelp instructions and request a quota increase http://www.yelp.com/developers/getting_started
@wowNetworks - Trulia and Altos are not APIs - the charts are just static images. So, if an image of a chart was displaying just fine at one moment and doesn't get displayed at another, I would guess it has something to do with Trulia or Altos. When you're initially creating charts using those resources, if there is no image being displayed in your page editor, that means that Trulia/Altos doesn't have that data.
One of our sites is using this plugin, and everything is being displayed correctly - http://www.scottsdalehomes.com/properties/kierland-greens-condo/ - it takes painfully long time to get everything loaded, but all tabs (eventually) get populated with data. Even if some tabs don't display data at first, just wait a few seconds and check them again.
If you can give me a temporary administrative access to your WordPress dashboard, I'll be happy to take a look at your site. Feel free to submit a support ticket with your site login info via this page: http://simplerealtytheme.com/support/