Database check yields warnings, mostly wrong use of index

These are the warnings:

Table w_users - check - warning -
Found row where the auto_increment column has the ...

Problems with indexes of table `w_blocks`
UNIQUE and INDEX keys should not both be set for column `theme`

Problems with indexes of table `w_filters`
UNIQUE and INDEX keys should not both be set for column `format`

Problems with indexes of table `w_menu_links`
More than one INDEX key was created for column `menu_name`

Problems with indexes of table `w_node`
PRIMARY and INDEX keys should not both be set for column `nid`

Problems with indexes of table `w_search_index`
UNIQUE and INDEX keys should not both be set for column `word`

Problems with indexes of table `w_system`
More than one INDEX key was created for column `type`

Problems with indexes of table `w_term_data`
More than one INDEX key was created for column `vid`

Problems with indexes of table `w_term_hierarchy`
PRIMARY and INDEX keys should not both be set for column `tid`

Problems with indexes of table `w_votingapi_cache`
More than one INDEX key was created for column `content_type`

Problems with indexes of table `w_votingapi_vote`
More than one INDEX key was created for column `content_type`

I think it is indeed not sensible to create more than one index for one table column. Or is there something behind it that the checker and I don't understand?