You can use only Jinja2 tests in selectattr:
http://jinja.pocoo.org/docs/2.9/templates/#builtin-tests http://docs.ansible.com/ansible/latest/playbooks_tests.html

For your example:

- debug:
    msg: "{{ item.name }}"
  with_items: "{{ network.addresses.private_man | selectattr('addr','issuperset',['1.2.3.4']) | list }}"

Edit: I actually didn't pay enough attention to the latest edit of the existing answer from @ranjandas and the following comments. My first solution is almost similar. I guess you are more interested by the second one.

Here are 2 different ways to achieve your requirement.

1. The first solution uses only filters available in ansible by default: rejectattr you already mentionned and its counterpart selectattr. The idea is to add two lists. The first one is made by selecting all dicts not having the type atttribute. The second one is made by selecting dict having the type attribute and rejecting those where it equals special.

2. For the second solution, I used the json_query filter which requires pip install jmespath on the controller. As you can see below it is much more compact.

The choice is yours !

The demo playbook:

---
- name: Show not so special items
  hosts: localhost
  gather_facts: false

  vars:
    list_of_dicts:
      - name: Item1
      - name: Item2
        type: special
      - name: Item3
      - name: Item4
        type: small

  tasks:
    - name: Use select/rejectattr
      debug:
        msg: >-
          {{
            (list_of_dicts | selectattr('type', 'undefined') | list)
            +
            (list_of_dicts | selectattr('type', 'defined') | rejectattr('type', 'eq', 'special') | list)
          }}

    - name: Use json_query
      vars:
        query: "[?type != 'special']"
      debug:
        msg: "{{ list_of_dicts | json_query(query) | list }}"

Which gives:

PLAY [Show not so special items] **********************************************************************************************************************************************************************************

TASK [Use select/rejectattr] **************************************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": [
        {
            "name": "Item1"
        },
        {
            "name": "Item3"
        },
        {
            "name": "Item4",
            "type": "small"
        }
    ]
}

TASK [Use json_query] *********************************************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": [
        {
            "name": "Item1"
        },
        {
            "name": "Item3"
        },
        {
            "name": "Item4",
            "type": "small"
        }
    ]
}

PLAY RECAP ********************************************************************************************************************************************************************************************************
localhost                  : ok=2    changed=0    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0

Is selectattr filter expecting all the dicts in the list to have the same keys?

More precisely, it is expecting all dicts in the list to have the attribute you are selecting on. If not all dict in the list have it, you will have to first filter out the items where it is not defined. This can be done with selectattr as well. (thanks @Randy for making this clearer since my initial answer).

In your situation, the json_query filter (which implements jmespath) can also do the job in sometimes a more compact manner. But it is not a core filter and requires to have the community.general collection installed.

Here are a few examples taken from your above requirements solved with both core filters and json_query solutions.

The playbook:

---
- name: "Filter data with core filters or json query"
  hosts: "localhost"
  gather_facts: false

  vars:
    # Your initial data on a single line for legibility
    test_var: [{"vm":"vm1","ip":"10.10.10.1"},{"vm":"vm2","ip":"10.10.10.2"},{"test_vm":"something","process_1":"X","process_2":"Y","process_3":"Z"},{"another_vm":"something_other"}]

  tasks:
    - name: Get objects having vm==vm1
      vars:
        msg: |-
          With core filters: {{ test_var | selectattr('vm', 'defined') | selectattr('vm', '==', 'vm1') | list }}
          With json_query: {{ test_var | json_query("[?vm=='vm1']") | list }}
      debug:
        msg: "{{ msg.split('\n') }}"

    - name: Get all objects having vm attribute
      vars:
        msg: |-
          With core filters: {{ test_var | selectattr('vm', 'defined') | list }}
          With json_query: {{ test_var | json_query("[?vm]") | list }}
      debug:
        msg: "{{ msg.split('\n') }}"

    - name: Get all objects having process_2 attribute
      vars:
        msg: |-
          With core filters: {{ test_var | selectattr('process_2', 'defined') | list }}
          With json_query: {{ test_var | json_query("[?process_2]") | list }}
      debug:
        msg: "{{ msg.split('\n') }}"

    - name: Get only a list of process_2 attributes
      vars:
        msg: |-
          With core filters: {{ test_var | selectattr('process_2', 'defined') | map(attribute='process_2') | list }}
          With json_query: {{ test_var | json_query("[].process_2") | list }}
      debug:
        msg: "{{ msg.split('\n') }}"

which gives:

PLAY [Filter data with core filters or json query] *********************************************************************

TASK [Get objects having vm==vm1] *********************************************************************
ok: [localhost] => {
    "msg": [
        "With core filters: [{'vm': 'vm1', 'ip': '10.10.10.1'}]",
        "With json_query: [{'vm': 'vm1', 'ip': '10.10.10.1'}]"
    ]
}

TASK [Get all objects having vm attribute] *********************************************************************
ok: [localhost] => {
    "msg": [
        "With core filters: [{'vm': 'vm1', 'ip': '10.10.10.1'}, {'vm': 'vm2', 'ip': '10.10.10.2'}]",
        "With json_query: [{'vm': 'vm1', 'ip': '10.10.10.1'}, {'vm': 'vm2', 'ip': '10.10.10.2'}]"
    ]
}

TASK [Get all objects having process_2 attribute] *********************************************************************
ok: [localhost] => {
    "msg": [
        "With core filters: [{'test_vm': 'something', 'process_1': 'X', 'process_2': 'Y', 'process_3': 'Z'}]",
        "With json_query: [{'test_vm': 'something', 'process_1': 'X', 'process_2': 'Y', 'process_3': 'Z'}]"
    ]
}

TASK [Get only a list of process_2 attributes] *********************************************************************
ok: [localhost] => {
    "msg": [
        "With core filters: ['Y']",
        "With json_query: ['Y']"
    ]
}

PLAY RECAP *********************************************************************
localhost                  : ok=4    changed=0    unreachable=0    failed=0    skipped=0    rescued=0    ignored=0