Hi again,
 
Now I am really confused. I am looking at texMate.py , and I am not
seeing neither a refreshViewer method, nor any mention of any
applescript terms.  In my version, /usr/bin/open is used, on line
111, in a method called run_viewer. In which lines of texMate.py
exactly are the applescript calls supposed to be at?

Ditto re the confusion: my texMate.py has "refreshViewer" defined on line 122 (and "run_viewer" on line 143). It's the texMate.py that's part of TextMate revision 1455. I've thrown a copy of the file texMate.py from

/Applications/TextMate.app/Contents/SharedSupport/Bundles/Latex.tmbundle/Support/bin

to

http://staff.maths.adelaide.edu.au/~pmccann/texMate.py


if you wish to try to decipher its provenance! There's an identical version of it contained within "texMate.app".

Cheers,
Paul