Combining 2 dictionaries with common key

All you need to do is to modify append to extend which will then add the elements of the list rather than adding the list itself. See the list docs for more details on the difference between append and extend.

dict1 = {'key1':['value11','value12','value13'] , 'key2':['value21','value22','value23']}
dict2 = {'key1':['value14','value15'] , 'key2':['value24','value25']}

dict3 = {}
for key in set().union(dict1, dict2):
    if key in dict1: dict3.setdefault(key, []).extend(dict1[key])
    if key in dict2: dict3.setdefault(key, []).extend(dict2[key])

print(dict3)
# {'key2': ['value21', 'value22', 'value23', 'value24', 'value25'], 'key1': ['value11', 'value12', 'value13', 'value14', 'value15']}

Alternatively you could use a collections.defaultdict with the default set to list as shown below.

from collections import defaultdict
dict3 = defaultdict(list)

for key in set().union(dict1, dict2):
  for dic in [dict1, dict2]:
    if key in dic:
      dict3[key] += dic[key]

You can do it much simpler but if you want to use your code just change append to extend

dict1 = {'key1':['value11','value12','value13'] , 'key2':['value21','value22','value23']}
dict2 = {'key1':['value14','value15'] , 'key2':['value24','value25']}

dict3 = {}
for key in (dict1.viewkeys() | dict2.keys()):
    if key in dict1: dict3.setdefault(key, []).extend(dict1[key])
    if key in dict2: dict3.setdefault(key, []).extend(dict2[key])

print dict3

output:

{'key2': ['value21', 'value22', 'value23', 'value24', 'value25'], 'key1': ['value11', 'value12', 'value13', 'value14', 'value15']}

You can read this post about the difference ov append to extend