BuddyPress.org

1. Which version of WordPress are you running? – 3.6 (but the problem was there before upgrading from 3.5.2)

2. Did you install WordPress as a directory or subdomain install? – N/A

3. If a directory install, is it in root or in a subdirectory? – N/A

4. Did you upgrade from a previous version of WordPress? If so, from which version? – 3.5.2

5. Was WordPress functioning properly before installing/upgrading BuddyPress (BP)? e.g. permalinks, creating a new post, commenting. – N/A

6. Which version of BP are you running? – 1.8.1

7. Did you upgraded from a previous version of BP? If so, from which version? – 1.8

8. Do you have any plugins other than BuddyPress installed and activated? If so, which ones? – Many but I have tried disabling them all except Buddypress and the problem is still there.

9. Are you using the standard BuddyPress themes or customized themes? – Customised theme but problem is persistent even with Twenty Twelve theme.

10. Have you modified the core files in any way? – No

11. Do you have any custom functions in bp-custom.php?

<?php
// hacks and mods will go here

function activity_publish_custom_post_types($cpts) {
   $cpts[] = 'page';
   $cpts[] = 'attachment';
   return $cpts;
}

add_filter ( 'bp_blogs_record_post_post_types', 'activity_publish_custom_post_types' );
add_filter ( 'bp_blogs_record_comment_post_types', 'activity_publish_custom_post_types' );

add_filter( ‘bp_get_total_member_count’, ‘bp_core_get_total_member_count’ );

?>

12. If running bbPress, which version? Or did your BuddyPress install come with a copy of bbPress built-in? – 2.3.2

13. Please provide a list of any errors in your server’s log files.

text/x-generic error_log 
ASCII English text, with very long lines
[31-Jul-2013 23:00:48 UTC] WordPress database error You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'WHERE meta_key = 'entry_id' AND meta_value = '211'' at line 1 for query SELECT site_id FROM  WHERE meta_key = 'entry_id' AND meta_value = '211' made by require('wp-blog-header.php'), wp, WP->main, WP->parse_request, do_action_ref_array, call_user_func_array, GFPMoreStripe::parse_request, GFPMoreStripe::cancel_subscription, do_action('gform_subscription_canceled'), call_user_func_array, GFPMoreStripe::downgrade_stripe_user, GFUserData::get_site_by_entry_id
[01-Aug-2013 04:22:39 UTC] wpMandrill Error: Error : 
[01-Aug-2013 04:22:39 UTC] 2013-08-01 04:22:39 wpMandrill::sendEmail: Exception Caught => Invalid API Key

[01-Aug-2013 04:22:39 UTC] blah@blah.com ([blah blah] Password Reset)

[01-Aug-2013 16:08:26 UTC] WordPress database error You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'WHERE meta_key = 'entry_id' AND meta_value = '217'' at line 1 for query SELECT site_id FROM  WHERE meta_key = 'entry_id' AND meta_value = '217' made by require('wp-blog-header.php'), wp, WP->main, WP->parse_request, do_action_ref_array, call_user_func_array, GFPMoreStripe::parse_request, GFPMoreStripe::cancel_subscription, do_action('gform_subscription_canceled'), call_user_func_array, GFPMoreStripe::downgrade_stripe_user, GFUserData::get_site_by_entry_id
[02-Aug-2013 13:43:45 UTC] wpMandrill Error: Error : 
[02-Aug-2013 13:43:45 UTC] 2013-08-02 13:43:45 wpMandrill::sendEmail: Exception Caught => Invalid API Key

[02-Aug-2013 13:43:45 UTC] 
wpMandrill::wp_mail_native: blah@blah.net ([blah blah] First Order)

[02-Aug-2013 17:07:36 UTC] wpMandrill Error: Error : 
[02-Aug-2013 17:07:36 UTC] 2013-08-02 17:07:36 wpMandrill::sendEmail: Exception Caught => Invalid API Key

[02-Aug-2013 17:07:36 UTC] 
wpMandrill::wp_mail_native: blah@blah.net ([blah blah] First Order)

[02-Aug-2013 21:57:15 UTC] wpMandrill Error: Error : 
[02-Aug-2013 21:57:15 UTC] 2013-08-02 21:57:15 wpMandrill::sendEmail: Exception Caught => Invalid API Key

[02-Aug-2013 21:57:15 UTC] 
wpMandrill::wp_mail_native: blah@blah.com (Welcome to blahblah!)

[06-Aug-2013 03:54:52 UTC] WordPress database error You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'WHERE meta_key = 'entry_id' AND meta_value = '265'' at line 1 for query SELECT site_id FROM  WHERE meta_key = 'entry_id' AND meta_value = '265' made by require('wp-blog-header.php'), wp, WP->main, WP->parse_request, do_action_ref_array, call_user_func_array, GFPMoreStripe::parse_request, GFPMoreStripe::cancel_subscription, do_action('gform_subscription_canceled'), call_user_func_array, GFPMoreStripe::downgrade_stripe_user, GFUserData::get_site_by_entry_id
[06-Aug-2013 13:23:34 UTC] WordPress database error Unknown column '$autopurge_interval' in 'where clause' for query DELETE ts FROM wp_slim_stats ts WHERE ts.dt < UNIX_TIMESTAMP(DATE_SUB(NOW(), INTERVAL $autopurge_interval DAY)) made by do_action_ref_array, call_user_func_array, wp_slimstat::wp_slimstat_purge

14. Which company provides your hosting? – OVH.com

15. Is your server running Windows, or if Linux; Apache, nginx or something else? – Apache

Thank you @mercime for your reply. I have disabled all plugins and used a fresh Twenty Twelve them and the problem is still there. Thanks in advance.