Metadata (exif data) can contain information about image rotation. Nowadays, this often is the case with images made on mobile phones. If you watch the images on your computer or phone the program you use might display the image taking into account the rotation information but not changing it.

During upload images with Tidypics the rotation information (if it exists) is used to rotate the image for real and save the image with correct orientation removing the rotation metadata. This way the images should be correctly displayed not only within browsers but also within programs not supporting any internal image orientation correction.

I'm not aware that there's any bug with image rotation within Tidypics (i.e. it works for me as expected). May I ask that you might try do a bit of testing yourself to see if you see any pattern. Does it happen with all users or only with specfiic users? In the latter case what's different with them with regard to images uploaded from desktop computers or directly from phones? Do you have the option to remove exif data prior upload enabled (image orientation should be fixed nonetheless but maybe something fails there)? Can you check if exif data exists before you upload an image and what happens with images taken with different orientation (e.g. by rotation the phone)?

I'm not sure but I believe I remember someone having the same or a very similar error only recently. In this case the error was causes by a 3rd party plugin, if I remember correctly (might have been some hype*** plugin). Have you tested what happens when you temporarily disable 3rd party plugins that might be responsible (e.g. adding any functionality to the wire or list pages in general)?

The Liberation theme seems to have a bug in start.php. See the latest comment at https://elgg.org/plugins/2511405/releases/160.2201.6. This should fix the login issue.

Regarding the other site I can't say anything not knowing which theme is used. Maybe the theme used also is buggy.