Some users may need to change their phone's permissions to allow the foursquare app to properly connect to the internet. If you are having issues signing into foursquare, etc. you can change your app permissions as follows:
On your BlackBerry, go to "Options" > "Advanced Options" > "Applications"
Scroll through the list to find the "FourSquare" app
Hit the menu button and select "Edit Permissions" from context menu
Change the permissions for "Connections", "Interactions" and "User Data" to "Allow"