I struggled a lot with upgrading a Joomla 2.5.28 installation from 2.5.28 to 3.4.1
I have added the error I got, when I updated through the Joomla updater, in a txt file.
After updating and receiving the error, you can still navigate back to the Joomla control panel, but when you try to access different areas such as article, extensions etc. you receive errors such as

Fatal error: Call to a member function get() on a non-object in home\site-name\administrator\components\com_content\controllers\article.php on line 34

Fatal error: Call to a member function get() on a non-object in home\sitename\administrator\components\com_installer\controller.php on line 37

I am not really sure what causes this error. But I'm more than willing to share my Akeeba Backup file, if anyone wants my test data. It's the first time I've had this much trouble updating a Joomla site, but one of my own colleagues had the same issue and gave me the following advice, which I have pasted below:

What I did to actually get the site up and running was the following
Step 1 : Disabled the "Remember me" plugin before migrating

Step2 : Download the update package from here: http://www.joomla.org/announcements/release-news/5468-joomla-3-0-1-released.html The one that say (for updates from Joomla 2.5)

Step3: Install the package through the Joomla installer

After that I could continue updating Joomla through the Joomla updater

EDIT.. the tracker did not allow me to upload the txt file. Here is the full text:
1062 - An error has occurred.

Duplicate entry '1' for key 'PRIMARY' SQL=-- -- Dumping data for table j25_content_types -- INSERT INTO j25_content_types (type_id, type_title, type_alias, table, rules,

field_mappings,router) VALUES (1, 'Article', 'com_content.article', '{"special":{"dbtable":"#__content","key":"id","type":"Content","prefix":"JTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"title","core_state":"state","core_alias":"alias","core_created_time":"created","core_modified_time":"modified","core_body":"introtext",

"core_hits":"hits","core_publish_up":"publish_up","core_publish_down":"publish_down","core_access":"access", "core_params":"attribs", "core_featured":"featured",

"core_metadata":"metadata", "core_language":"language", "core_images":"images", "core_urls":"urls", "core_version":"version", "core_ordering":"ordering", "core_metakey":"metakey",

"core_metadesc":"metadesc", "core_catid":"catid", "core_xreference":"xreference", "asset_id":"asset_id"}], "special": [{"fulltext":"fulltext"}]}','ContentHelperRoute::getArticleRoute'),

(2, 'Contact', 'com_contact.contact', '{"special":{"dbtable":"#__contact_details","key":"id","type":"Contact","prefix":"ContactTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"name","core_state":"published","core_alias":"alias","core_created_time":"created","core_modified_time":"modified","core_body":"address",

"core_hits":"hits","core_publish_up":"publish_up","core_publish_down":"publish_down","core_access":"access", "core_params":"params", "core_featured":"featured",

"core_metadata":"metadata", "core_language":"language", "core_images":"image", "core_urls":"webpage", "core_version":"version", "core_ordering":"ordering", "core_metakey":"metakey",

"core_metadesc":"metadesc", "core_catid":"catid", "core_xreference":"xreference", "asset_id":"null"}], "special":

[{"con_position":"con_position","suburb":"suburb","state":"state","country":"country","postcode":"postcode","telephone":"telephone","fax":"fax","misc":"misc","email_to":"email_to","defau

lt_con":"default_con","user_id":"user_id","mobile":"mobile","sortname1":"sortname1","sortname2":"sortname2","sortname3":"sortname3"}]}','ContactHelperRoute::getContactRoute'), (3,

'Newsfeed', 'com_newsfeeds.newsfeed', '{"special":{"dbtable":"#__newsfeeds","key":"id","type":"Newsfeed","prefix":"NewsfeedsTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"name","core_state":"published","core_alias":"alias","core_created_time":"created","core_modified_time":"modified","core_body":"description",

"core_hits":"hits","core_publish_up":"publish_up","core_publish_down":"publish_down","core_access":"access", "core_params":"params", "core_featured":"featured",

"core_metadata":"metadata", "core_language":"language", "core_images":"images", "core_urls":"link", "core_version":"version", "core_ordering":"ordering", "core_metakey":"metakey",

"core_metadesc":"metadesc", "core_catid":"catid", "core_xreference":"xreference", "asset_id":"null"}], "special":

[{"numarticles":"numarticles","cache_time":"cache_time","rtl":"rtl"}]}','NewsfeedsHelperRoute::getNewsfeedRoute'), (4, 'User', 'com_users.user', '{"special":

{"dbtable":"#__users","key":"id","type":"User","prefix":"JTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"name","core_state":"null","core_alias":"username","core_created_time":"registerdate","core_modified_time":"lastvisitDate","core_body":"null",

"core_hits":"null","core_publish_up":"null","core_publish_down":"null","access":"null", "core_params":"params", "core_featured":"null", "core_metadata":"null", "core_language":"null",

"core_images":"null", "core_urls":"null", "core_version":"null", "core_ordering":"null", "core_metakey":"null", "core_metadesc":"null", "core_catid":"null", "core_xreference":"null",

"asset_id":"null"}], "special": [{}]}','UsersHelperRoute::getUserRoute'), (5, 'Article Category', 'com_content.category', '{"special":

{"dbtable":"#__categories","key":"id","type":"Category","prefix":"JTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"title","core_state":"published","core_alias":"alias","core_created_time":"created_time","core_modified_time":"modified_time","core_body":"desc

ription", "core_hits":"hits","core_publish_up":"null","core_publish_down":"null","core_access":"access", "core_params":"params", "core_featured":"null", "core_metadata":"metadata",

"core_language":"language", "core_images":"null", "core_urls":"null", "core_version":"version", "core_ordering":"null", "core_metakey":"metakey", "core_metadesc":"metadesc",

"core_catid":"parent_id", "core_xreference":"null", "asset_id":"asset_id"}], "special":

[{"parent_id":"parent_id","lft":"lft","rgt":"rgt","level":"level","path":"path","extension":"extension","note":"note"}]}','ContentHelperRoute::getCategoryRoute'), (6, 'Contact Category',

'com_contact.category', '{"special":{"dbtable":"#__categories","key":"id","type":"Category","prefix":"JTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"title","core_state":"published","core_alias":"alias","core_created_time":"created_time","core_modified_time":"modified_time","core_body":"desc

ription", "core_hits":"hits","core_publish_up":"null","core_publish_down":"null","core_access":"access", "core_params":"params", "core_featured":"null", "core_metadata":"metadata",

"core_language":"language", "core_images":"null", "core_urls":"null", "core_version":"version", "core_ordering":"null", "core_metakey":"metakey", "core_metadesc":"metadesc",

"core_catid":"parent_id", "core_xreference":"null", "asset_id":"asset_id"}], "special":

[{"parent_id":"parent_id","lft":"lft","rgt":"rgt","level":"level","path":"path","extension":"extension","note":"note"}]}','ContactHelperRoute::getCategoryRoute'), (7, 'Newsfeeds

Category', 'com_newsfeeds.category', '{"special":{"dbtable":"#__categories","key":"id","type":"Category","prefix":"JTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"title","core_state":"published","core_alias":"alias","core_created_time":"created_time","core_modified_time":"modified_time","core_body":"desc

ription", "core_hits":"hits","core_publish_up":"null","core_publish_down":"null","core_access":"access", "core_params":"params", "core_featured":"null", "core_metadata":"metadata",

"core_language":"language", "core_images":"null", "core_urls":"null", "core_version":"version", "core_ordering":"null", "core_metakey":"metakey", "core_metadesc":"metadesc",

"core_catid":"parent_id", "core_xreference":"null", "asset_id":"asset_id"}], "special":

[{"parent_id":"parent_id","lft":"lft","rgt":"rgt","level":"level","path":"path","extension":"extension","note":"note"}]}','NewsfeedsHelperRoute::getCategoryRoute'), (8, 'Tag',

'com_tags.tag', '{"special":{"dbtable":"#__tags","key":"tag_id","type":"Tag","prefix":"TagsTable","config":"array()"},"common":

{"dbtable":"#__core_content","key":"ucm_id","type":"Corecontent","prefix":"JTable","config":"array()"}}', '', '{"common":

[{"core_content_item_id":"id","core_title":"title","core_state":"published","core_alias":"alias","core_created_time":"created_time","core_modified_time":"modified_time","core_body":"desc

ription", "core_hits":"hits","core_publish_up":"null","core_publish_down":"null","core_access":"access", "core_params":"params", "core_featured":"featured", "core_metadata":"metadata",

"core_language":"language", "core_images":"images", "core_urls":"urls", "core_version":"version", "core_ordering":"null", "core_metakey":"metakey", "core_metadesc":"metadesc",

"core_catid":"null", "core_xreference":"null", "asset_id":"null"}], "special":

[{"parent_id":"parent_id","lft":"lft","rgt":"rgt","level":"level","path":"path"}]}','TagsHelperRoute::getTagRoute');