So, I recently had an issue with a failure with updating to Joomla 3.6.5. It looks like I was mostly able to recover from the error by manually updating, however there seem to be issues with the database. Fixing the database just produces more errors, and thus isn't a option.
Error
Table 'greentec.#__updates' doesn't exist SQL=SHOW COLUMNS IN `#__updates` WHERE field = 'infourl'
Table 'greentec.#__updates' doesn't exist SQL=SHOW COLUMNS IN `#__updates` WHERE Field = 'categoryid'
Table 'greentec.#__updates' doesn't exist SQL=SHOW COLUMNS IN `#__updates` WHERE field = 'extra_query'
Table 'greentec.#__updates' doesn't exist SQL=SHOW COLUMNS IN `#__updates` WHERE field = 'version' AND type = 'varchar(32)'
and the following list of database problems:
Database schema version (3.4.0-2015-02-26) does not match CMS version (3.6.3-2016-08-16).
Database update version (3.4.8) does not match CMS version (3.6.5).
Table 'zyjgk_updates' does not have column 'infourl'. (From file 2.5.0-2012-01-10.sql.)
Table 'zyjgk_updates' should not have column 'categoryid'. (From file 3.0.0.sql.)
Table 'zyjgk_updates' does not have column 'extra_query'. (From file 3.2.2-2013-12-22.sql.)
Table 'zyjgk_updates' does not have column 'version' with type varchar(32). (From file 3.2.2-2014-01-18.sql.)
Table 'zyjgk_session' does not have column 'session_id' with type varchar(191). (From file 3.5.0-2015-07-01.sql.)
Table 'zyjgk_user_keys' does not have column 'series' with type varchar(191). (From file 3.5.0-2015-07-01.sql.)
Table 'zyjgk_contentitem_tag_map' should not have index 'idx_tag'. (From file 3.5.0-2015-10-26.sql.)
Table 'zyjgk_contentitem_tag_map' should not have index 'idx_type'. (From file 3.5.0-2015-10-26.sql.)
Table 'zyjgk_redirect_links' should not have index 'idx_link_old'. (From file 3.5.0-2016-03-01.sql.)
Table 'zyjgk_redirect_links' does not have column 'old_url' with type VARCHAR(2048). (From file 3.5.0-2016-03-01.sql.)
Table 'zyjgk_redirect_links' does not have column 'new_url' with type VARCHAR(2048);. (From file 3.5.0-2016-03-01.sql.)
Table 'zyjgk_redirect_links' does not have column 'referer' with type VARCHAR(2048). (From file 3.5.0-2016-03-01.sql.)
Table 'zyjgk_redirect_links' does not have index 'idx_old_url'. (From file 3.5.0-2016-03-01.sql.)
Table 'zyjgk_user_keys' does not have column 'user_id' with type varchar(150). (From file 3.5.1-2016-03-25.sql.)
Table 'zyjgk_redirect_links' does not have column 'new_url' with type VARCHAR(2048);. (From file 3.6.0-2016-04-06.sql.)
Table 'zyjgk_menu_types' does not have column 'asset_id'. (From file 3.6.0-2016-04-09.sql.)
Table 'zyjgk_languages' does not have column 'asset_id'. (From file 3.6.0-2016-06-05.sql.)
Table 'zyjgk_newsfeeds' does not have column 'link' with type VARCHAR(2048). (From file 3.6.3-2016-08-15.sql.)
The Joomla! Core database tables have not been converted yet to UTF-8 Multibyte (utf8mb4).
The site seem to be functioning for now, but I get database errors when I try to run an update, so I'm sure of how to proceed.