There's something I'm not doing right. I am importing info from 3 data fields from a related record via script. If I run the script 'with dialog' and set everything up, the import runs fine, I then test run again without dialog and everything is great...until I close the databases then reopen them, the data is now brought into incorrect fields. (I find the 'replace..keep' dialog encountered after the dialog change to be confusing). What am I missing here?

You need to go back into the script and check 'Replace'. Replace means to replace the script's saved specs (whether they're printing, sorting, importing, etc.) with the one that is currently in effect...basically the last time you ran anything by hand (clicked on import on the file menu, went thru print setup, sorted the found set, etc.)