I did not take the time to format things pretty for you, but here is a quick and dirty way to sort these. Since your dates are formatted in a nice way, they can be sorted easily. This is not as efficient as the other answers, because I am constructing a whole new dictionary with redundant data.
list_of_dicts = []
dict1 = {'Source': 'Log1', 'Type': 'Connection', 'Datetime': '2014-02-13 14:10:00', 'fullpath':'N/A'}
dict2 = {'Source': 'Log2', 'Type': 'Disconnect', 'Datetime': '2014-05-13 11:00:00', 'fullpath':'N/A'}
dict3 = {'Source': 'Log4', 'Type': 'Other', 'Datetime': '2014-05-10 02:50:00', 'fullpath':'N/A'}
list_of_dicts.append(dict1)
list_of_dicts.append(dict2)
list_of_dicts.append(dict3)
d = {d['Datetime']:d for d in list_of_dicts} # dictionary comprehension
for k in sorted(d.keys()):
print(d[k])