I have latest 1.2.5 zenphoto installed. Everything works perfectly except Image info link. Nothing opens. I haven't modified image.php page. EXIF info has not been removed from the images. Currently it looks like this:

So, is there any HTML produced by printImageMetadata()? If not, then your image has no metadata. If so and it is not displaying, then you have a problem with your CSS.

Clicking to the link won't even open a new window. Only the address bar changes for example to this: http://www.soida.ee/gallery/teised-elukad/DSC_0008_copy.JPG.php#TB_inline?height=345&width=300&inlineId=imagemetadata

The same picture in my PC consists EXIF info.

Since you seem to use a modified default theme you should try an unmodified one and then find the difference. It is generally working as you can see on our demo: http://www.zenphoto.org/zenphoto/demo-gallery/P4100284.jpg.php

I tried default and zenpage-default original themes and none of these were working.
Is it possible to enable some debug mode to see any kind of error messages?

Seems like the thickbox is not working. Check to see if you have any Javascript errors. Could also be a problem with your CSS.

You were right. Entering to that image page I got quite a lot of thickbox.css errors.
Printscreen is here http://www.soida.ee/files/jserror.jpg

It is fixed now! For some reason tag.js was damaged (file size difference). Now everything looks OK.
Thanks for the effort!