Foursquare does not offer a way to handle your friend requests in bulk. You'll have to individually hit those Accept or Ignore buttons, which is a tedious task -- unless you use this nifty workaround.
Amit Agarwal of Digital Inspiration has a neat trick to accept or ignore all requests:
- Go to the Foursquare.com website and choose Friends -> See All Friend Requests
- While inside the console, type
$US('.orangeButton').click()to accept all requests or
$US('.greyButtton').click()to ignore all the requests.
Be warned that there is still no way to selectively check boxes and apply actions. In my case, the list of requests I wanted to ignore was three times as long as those I wanted to accept, so I quickly hit Accept wherever necessary and then used Amit's hack to ignore all the others. You could take the opposite approach if you have more requests to accept than ignore.
An Easy Way to Deal with Friend Requests on Foursquare [Digital Inspiration]