I search with the twitter API all the public tweets with "4sq.com":
so I get all the check-in on Foursquare that actually shared on Twitter.
{"created_at":"Sun, 08 Jan 2012 20:05:27 +0000","from_user":"fenavergara","from_user_id":50876086,"from_user_id_str":"50876086","from_user_name":"Fernanda Vergara Ch","geo":null,"id":156104246239051776,"id_str":"156104246239051776","iso_language_code":"lt","metadata":{"result_type":"recent"},"profile_image_url":"http://a2.twimg.com/profile_images/1708744785/image_normal.jpg","profile_image_url_https":"https://si0.twimg.com/profile_images/1708744785/image_normal.jpg","source":"<a href="http://foursquare.com" rel="nofollow">foursquare</a>","text":"I'm at Roca Roja (Antofagasta) http://t.co/DIKdYGwD","to_user":null,"to_user_id":null,"to_user_id_str":null,"to_user_name":null},{"created_at":"Sun, 08 Jan 2012 20:05:27 +0000","from_user":"Fabioland76","from_user_id":357326176,"from_user_id_str":"357326176","from_user_name":"Fabio Landini","geo":null,"id":156104246104821760,"id_str":"156104246104821760","iso_language_code":"no","metadata":{"result_type":"recent"},"profile_image_url":"http://a3.twimg.com/profile_images/1506958638/profiloJPG_normal.jpg","profile_image_url_https":"https://si0.twimg.com/profile_images/1506958638/profiloJPG_normal.jpg","source":"<a href="http://foursquare.com" rel="nofollow">foursquare</a>","text":"I'm at Burger King (Gallerie Cantoni, Legnano) http://t.co/rU1jIJ4A","to_user":null,"to_user_id":null,"to_user_id_str":null,"to_user_name":null}
With these tweets, Foursquare provides a link (like this one: http://t.co/DIKdYGwD) where I can see the position of the check-in on a map (if I display the link on a webpage).
How can I get the latitude and longitude programmaticly directly from the list of tweets?
Idea: Do I need to fetch the link on a webpage and analyse it to get the latitude and longitude?
EDIT: I don't want to use Twitter geocode
You already have what you want, look at the "geo" section in sample of search output you posted. It's null because it is not filled (twitter user forget to enable twitter location in settings and all locations from foursquare are ignored by twitter).
You can filter twits by location, look at the Twitter Dev documentation.
UPD:
If you want to get location even in case when it is not stored to twit, you have to perform request to foursquare short link and parse venue information (you can steal location also). Look at the source of the sample 4sq.com page (small part):
Unfortunately, Foursquare team can change the format of the page or limit requests from IP Address without any notes. That's why this solution is ugly.
UPD2
See answer from @MikeLewis, I've missed that Foursquare API supports requesting information by checking id.
There's actually a much nicer solution here if you would like to use the foursquare API. One that doesn't depend upon a user having enabled Twitter's geo-tagging.
You noticed already that the link in the status update redirects to a foursquare page. Rather than screen scraping, you may notice there are two key pieces of information in the url. The checkin id, and a parameter called s (for signature) that lets you access that checkin via foursquare's API.
https://foursquare.com/dens/checkin/4f0b3676e4b0e8ed3a590e41?s=MWHM3-0BsLXIJprfbALvOM606ZE&ref=tw
For instance, in the above url, the checkin id is 4f0b3676e4b0e8ed3a590e41 while the signature is MWHM3-0BsLXIJprfbALvOM606ZE
Using the /checkins endpoint, you can get the full checkin details (including lat/long of the venue). Dox here: https://developer.foursquare.com/docs/checkins/checkins