how to start diagnosing a possibly corrupted site?

Hi all,
I actually love puzzling out bugs, but sometimes the way they manifest is just too obscure. Ive got one of those now on a D7.30 site, so I'd love to hear different strategies for narrowing down the search field, not just for this particular issue, but generally, since I imagine this might help others too.

The actual issue:
A new content type with standard (core) image field does not respect any changes to the list of allowed upload file types. E.g. if I add TIF to the list, it appears in the content type ok but when creating new content, it wont allow TIFs. I also noticed that the new content type appears in the Add Content submenu but at the end of the submenu (ie NOT in alphabetical order).

My thinking is along these lines:

Ok I am pretty confident that despite manifesting as a core image field issue, this isn't really a core issue, so its either contrib or environment.

Main suspects are misbehaving contrib module, or an issue with database-stored config. Cleared cache multiple times. Did a quick phpMySql check of database tables and no corruption at that level. But not sure how to check if config stored in DB is dodgy.

Other recent environmental changes : turned on Views_Slideshow module, created new content type, new view, new content, changed some CSS, did an import with Feeds. Also server's security cert just expired. And the weather's gotten a bit more autumnal in Wicklow today ;-)

Drupal status report is happy.

Modules: Ok, I've got a bunch of contrib modules and one custom module in this installation. AFAIK none of these are invoked when I'm creating a new instance of my new content type. Modules include Views Ctools Feeds, Field Collection, Field Collection Table, Entity Reference, Multiupload FileField, Media, Minipanels, Rules, Lightbox, Views Slideshow, etc. My custom module is only used for remote authentication.

Widget: If I change to Media Widget the file type IS respected; it seems to only be the core Image widget that isn't behaving right.

Logs: Only errors of any note in logs today are related to lightbox, here's an example:
Notice: Undefined index: original in lightbox2_field_formatter_settings_summary() (line 897 of /home/.../public_html/sites/all/modules/lightbox2/lightbox2.module).

Older error that might be relevant:
Warning: Invalid argument supplied for foreach() in field_view_mode_settings() (line 627 of ...field.module).

So one possible strategy would be to turn off modules one by one until the error goes away. I'm going to do that and will report back. But it would be great to hear about & discuss other approaches to this sort of thing.

Mike