I suggest not using a reserved word like tuple as a variable name. It can be confusing.

The no attribute __getitem__ error comes from trying to get an element from a datetime object as if it were a list object: date_object[0].

How do I refer to the different dates if not by date_object[0] and date_object[-1]?

Okay now I get a new error:
Traceback (most recent call last):
File "<pyshell#68>", line 1, in
yelpclusterfinder.days_between_events('C:\Python27\TRUNCATED.txt', 1)
File "yelpclusterfinder.py", line 56, in days_between_events
date_delta = datetime.strptime(dates[0],('%Y-%m-%d'))-datetime.strptime(dates[-1],('%Y-%m-%d'))
File "C:\Python27\Lib_strptime.py", line 325, in _strptime
(data_string, format))
ValueError: time data '2' does not match format '%Y-%m-%d'
How do I format the 2nd date?

It looks like dates[-1] is returning the string '2' instead of what you expect.

First, get the import statements out of the functions and use a different variable name than tuple.
Second, debug step by step, making absolutely sure each line is doing what you expect. You can use unit tests (http://docs.python.org/2/library/unittest.html) if you feel like "doing it right", or just throw print statements everwhere, which is what many people do.

This probably doesn't work as-is, but it's moving in the direction of simpler functions that are easier to debug.

from collections import defaultdict

def parse_date(datestring):
    return datetime.strptime(datestring, '%Y-%m-%d')

def parse_events(filename):
    openfile = open(filename, "rU")
    regex = r'(\d{4}[-/]\d{2}[-/]\d{2})(.+)(\"business_id\"\: \".{22}\"\})'
    event_tuples = re.findall(regex, openfile.read())
    return event_tuples

def key_events_on_biz(event_tuples):
    event_dictionary = defaultdict(list)
    for fields in events:
        businessid = fields[2]
        date = field[0]
        event_dictionary[businessid].append(date)
    return event_dictionary

def diff_dates(event_dictionary):
    differences = {}
    for biz, datelist in event_dictionary.iteritems():
        first = parse_date(datelist[0])
        last = parse_date(datelist[-1])
        delta = last - first
        differences[biz] = delta
    return differences

if __name__ == "__main__":
    event_tuples = parse_events(filename)
    event_dictionary = key_events_on_biz(event_tuples)
    differences = diff_dates(event_dictionary)