WordPress listens to both $_GET and $_POST when parsing a request. If your form input names are conflicting with native query parameters, you’ll send WordPress on a wild goose chase (and most likely end up with a 404).
For your leisure, I’ve kindly listed them here – if any one of your form inputs uses these for a name, that’s the troublemaker.
Array
(
[0] => m
[1] => p
[2] => posts
[3] => w
[4] => cat
[5] => withcomments
[6] => withoutcomments
[7] => s
[8] => search
[9] => exact
[10] => sentence
[11] => debug
[12] => calendar
[13] => page
[14] => paged
[15] => more
[16] => tb
[17] => pb
[18] => author
[19] => order
[20] => orderby
[21] => year
[22] => monthnum
[23] => day
[24] => hour
[25] => minute
[26] => second
[27] => name
[28] => category_name
[29] => tag
[30] => feed
[31] => author_name
[32] => static
[33] => pagename
[34] => page_id
[35] => error
[36] => comments_popup
[37] => attachment
[38] => attachment_id
[39] => subpost
[40] => subpost_id
[41] => preview
[42] => robots
[43] => taxonomy
[44] => term
[45] => cpage
[46] => post_type
)