I am using ATA 3.5.3 on my blog (which I have been neglecting recently). Today it showed an error msg in the rotating header section about eregi being deprecated. A web search revealed that eregi should be replaced with preg_match, which I applied to line 33 of bfa_rotating_header_images.php. I am now getting the following error msg:

Warning: preg_match() [function.preg-match]: No ending delimiter '.' found in /home/coudr3/public_html/media-organic/wp-content/themes/atahualpa353/functions/bfa_rotating_header_images.php on line 33

This looks like it should be an easy fix but I've tried a few things and they have not been successful. Any help would be much appreciated.

I'm not sure what the implications are of making that change. Have you considered a manual update to 3.7.9 or perhaps seeing if all patches, if any, for 3.5.3 are applied.