Hi Nick, yes, I always make sure I have the latest up-to-date versions of Wordpress and all of my plug-ins. In fact my site is set up to automatically alert me as soon as a new version of anything is released, and I can do automatic updates as well. I do the same with my themes.
As far as the error log errors go, I don't have the expertise to understand what they actually refer to and consequently I can't always remedy them - I think I have found an expert who can help me if I can't sort this out for myself.
I can ask my host if they have updated the PHP part on their server, although I am not sure I will get a detailed enough response. They host thousands of photographers so I'm curious to know if others are having the same problems, but an Internet search hasn't revealed anything unfortunately.
Thank you again to everybody for the assistance, it really is appreciated. It's also helping me to learn a bit more about how these things work.
A couple of the most recent errors from the public_html/blog/error_log:
[09-Dec-2013 15:41:19] WordPress database error MySQL server has gone away for query UPDATE wp_blc_links SET url = 'http://lindsaydobsonphotography.com/blog/wp-content/uploads/2013/11/Sheffield-Park-241113-WEB-1350.jpg', first_failure = '0000-00-00 00:00:00', last_check = '2013-12-06 15:39:26', last_success = '2013-12-06 15:39:26', last_check_attempt = '2013-12-09 15:41:19', check_count = 1, final_url = 'http://lindsaydobsonphotography.com/blog/wp-content/uploads/2013/11/Sheffield-Park-241113-WEB-1350.jpg', redirect_count = 0, log = '=== HTTP code : 200 ===\n\nHTTP/1.1 200 OK\r\nDate: Fri, 06 Dec 2013 15:39:26 GMT\r\nServer: Apache/2.2.24 (Unix) mod_ssl/2.2.24 OpenSSL/1.0.0-fips mod_bwlimited/1.4\r\nLast-Modified: Sun, 24 Nov 2013 17:50:41 GMT\r\nETag: \"3dc321-bd32f-4ebefe2c33e40\"\r\nAccept-Ranges: bytes\r\nContent-Length: 774959\r\nContent-Type: image/jpeg\r\n\r\n\nLink is valid.', http_code = 200, request_duration = 0.001389, timeout = 0, result_hash = '200|0|0|160b3577ccf9f82a0a0f59ad24017dca', broken = 0, false_positive = 0, may_recheck = 1, being_checked = 1, status_text = '', status_code = '', dismissed = 0 WHERE link_id=6761 made by do_action_ref_array, call_user_func_array, wsBrokenLinkChecker->cron_check_links, wsBrokenLinkChecker->work, blcLink->check, blcLink->save
[09-Dec-2013 15:41:20] WordPress database error MySQL server has gone away for query UPDATE wp_blc_links SET url = 'http://lindsaydobsonphotography.com/blog/wp-content/uploads/2013/11/Sheffield-Park-241113-WEB-1350.jpg', first_failure = '0000-00-00 00:00:00', last_check = '2013-12-09 15:41:19', last_success = '2013-12-09 15:41:19', last_check_attempt = '2013-12-09 15:41:19', check_count = 0, final_url = 'http://lindsaydobsonphotography.com/blog/wp-content/uploads/2013/11/Sheffield-Park-241113-WEB-1350.jpg', redirect_count = 0, log = '=== HTTP code : 200 ===\n\nHTTP/1.1 200 OK\r\nDate: Mon, 09 Dec 2013 15:41:19 GMT\r\nServer: Apache/2.2.24 (Unix) mod_ssl/2.2.24 OpenSSL/1.0.0-fips mod_bwlimited/1.4\r\nLast-Modified: Sun, 24 Nov 2013 17:50:41 GMT\r\nETag: \"3dc321-bd32f-4ebefe2c33e40\"\r\nAccept-Ranges: bytes\r\nContent-Length: 774959\r\nContent-Type: image/jpeg\r\n\r\n\nLink is valid.', http_code = 200, request_duration = 0.001586, timeout = 0, result_hash = '200|0|0|160b3577ccf9f82a0a0f59ad24017dca', broken = 0, false_positive = 0, may_recheck = 1, being_checked = 0, status_text = '', status_code = '', dismissed = 0 WHERE link_id=6761 made by do_action_ref_array, call_user_func_array, wsBrokenLinkChecker->cron_check_links, wsBrokenLinkChecker->work, blcLink->check, blcLink->save
[09-Dec-2013 15:41:20] WordPress database error MySQL server has gone away for query SELECT links.*
The problem is that the errors keep changing (I don't even know if this is a PHP error), I can't keep up with them. Interestingly the error above seems to relate to a plug-in I installed two days ago to help me find and fix broken links on my website - it appears to work quite well, so I'm not sure why it's giving these errors.