Some needed options not available in field settings

I'm thinking this is a Views UI thing, but if it belongs somewhere else I'd be grateful for a pointer.

I'm editing a view that was originally built by the previous developer on my project.
In my dev environment, I can set certain options for fields exposed by my view; but in my production site, those options are gone from the interface.
Dev and production are on the same server.

Specifically:

1. I'm adding an image field that has unlimited instances in the content type. Normally I'd expect some settings in the Multiple Field Settings section to allow me to set both the number of images displayed, and the offset (1st one, second one, etc.) These options appear, and work fine, on the dev site. However on the production site these options simply don't appear (see screen shot).
2. I have a text field that I'd like to trim. The "Trim this field..." check box is there, but there's no option for number of characters, trim only on word breaks, add an ellipsis, etc. (See other screen shot).

I have no idea even how to go about debugging this, so any pointers will be greatly appreciated.